diff --git a/fremtex.tex b/fremtex.tex index 2983fe2..5476f35 100755 --- a/fremtex.tex +++ b/fremtex.tex @@ -116,12 +116,6 @@ \noindent e-mail: {\tt fremdh\@essex.ac.uk} %{\tt fremlin\@math.wisc.edu} \bigskip} -\long\def\homeaddress#1{\hskip 3truein 25 Ireton Road\par - \hskip 3truein Colchester CO3 3AT\par - \hskip 3truein England\par - \hskip 3.2truein#1\par - \noindent e-mail: {\tt fremdh\@essex.ac.uk} - \bigskip} \long\def\letterhead#1#2#3{\univaddress{#1} {\parindent=0pt #2 @@ -393,9 +387,8 @@ % or \Bover1{\sqrt{2\pi}^r} , these can sometimes come out with better % horizontal alignment if you use \Bover1{{\sshortstrut 2}^m} or % \Bover1{{\sqrt{2\pi}}^r} -\def\bsover#1#2{\textstyle\bover{#1}{#2}} +\def\bsover#1#2{\hbox{${#1}\over{#2}$}} \def\bsp{/\penalty-100} -\def\bsdot{.\penalty-100} \def\Caption{} \def\Center#1{ @@ -429,7 +422,6 @@ \def\cf{\mathop{\text{cf}}} \def\circumflex#1{{\accent"5E #1}} \def\closeplus{\hbox{+}} -\long\def\cmmnt#1{\ifresultsonly\else{#1}\fi} \def\coint#1{\left[#1\right[} \def\curl{\mathop{\text{curl}}} \def\dashint{\mathchoice{-\mskip-20mu\intop\nolimits} @@ -449,11 +441,11 @@ {\dashint\mskip-6mu\dashint} %not yet used {\dashint\mskip-6mu\dashint}} %not yet used \def\dashidashiint{\mathchoice{\dashint\mskip-8mu\dashint\mskip-10mu\int} - {\dashint\mskip-4mu\dashint\mskip-8mu\int} + {\dashint\mskip-6mu\int} %not yet used {\dashint\mskip-6mu\int} %not yet used {\dashint\mskip-6mu\int}} %not yet used \def\dashiidashint{\mathchoice{\dashint\mskip-10mu\int\mskip-8mu\dashint} - {\dashint\mskip-4mu\dashint\mskip-8mu\int} + {\dashint\mskip-6mu\int} %not yet used {\dashint\mskip-6mu\int} %not yet used {\dashint\mskip-6mu\int}} %not yet used \def\idashidashint{\mathchoice{\int\mskip-8mu\dashint\mskip-8mu\dashint} @@ -519,7 +511,7 @@ #1 {\vskip 1pt plus 1pt minus 0pt}}} \def\Int#1#2{\displaystyle{\int_{#1}^{#2}}} -\def\interior{\mathop{\text{int}}} +\def\interior{\mathop{\text{int}}\nolimits} \def\leae{\le_{\text{a.e.}}} \long\def\leaveitout#1{} diff --git a/mt.tex b/mt.tex index efa9cc3..79945b4 100755 --- a/mt.tex +++ b/mt.tex @@ -351,8 +351,7 @@ %note: neither \cal nor \eusm has lower case \def\CalFr{\Cal F_{\text{Fr}}} \def\callal{c\`all\`al} -\def\CalNwd{\Cal{N}\hskip-1.2pt\eurm{w}\hskip-.8pt\eurm{d}} - +\def\CalNwd{\Cal{N}\hskip-1.2pt\eurm{w}\hskip-.8pt\eurm{d}} \def\CalRbg{\Cal{R}\mskip-1mu\eurm{b}\mskip-1mu\eurm{g}} \def\CalSmz{\Cal{S}\mskip-2mu\eurm{mz}} \def\CalUn{\Cal{U}\eurm{n}} @@ -402,7 +401,6 @@ \else\ifnum\stylenumber=5{\frnewpage} \else\wheader{}{18}{14}{2}{72pt}\fi\fi\fi} \def\displaycause#1{\noalign{\noindent (#1)}} -\def\Displaycause#1{\cr\displaycause{#1}&} \def\dotproduct{\hskip.1em\tbf{.}\hskip.1em} \def\doubleheadrightarrow{\rightarrow\mskip-12mu\rightarrow} \long\def\doubleinset#1{\inset{\inset{\parindent=-20pt #1}}} @@ -454,7 +452,6 @@ {\hbox{$\scriptstyle<$}#1\hbox{$\scriptstyle>$}} {\hbox{$\scriptscriptstyle<$}#1\hbox{$\scriptscriptstyle>$}}} \def\frakmctbl{\frak m_{\text{countable}}} -\def\frmedcirc{{\raise 2.5pt\hbox{$_{\bigcirc}$}}} \def\grad{\mathop{\text{grad}}\nolimits} \def\Heint{\mathchoice{\hbox to 0pt{\hskip 3.1pt H\hss}} {\raise 0.6pt\hbox to 0pt{\hskip 1.9pt{\sevenrm H}\hss}} @@ -472,9 +469,9 @@ \def\innerprod#1#2{(#1|#2)} \def\intstar{\text{int*}} \def\jump{\mathop{\text{jump}}\nolimits} +\def\Jump{\mathop{\text{Jump}}\nolimits} \def\Krein{Kre\v{\i}n} -\def\leRB{\le_{\text{RB}}} -\def\leRK{\le_{\text{RK}}} +\def\Lambdapv{\Lambda_{\text{pv}}} \def\link{\mathord{\text{link}}} \def\locmafp{\widehat{\otimes}_{\text{loc}}} \def\Locmafp{\widehat{\bigotimes}^{\text{loc}}} @@ -496,6 +493,8 @@ \def\Mlob{M_{\text{lob}}} \def\Mns{M_{\text{n-s}}} \def\Mob{M_{\text{ob}}} +\def\Mpv{M_{\text{pv}}} +\def\MSi{M_{\text{S-i}}} \def\Msimp{M_{\text{simp}}} \def\Mth{Ma\-ha\-ram-{\vthsp}type-{\vthsp}homogeneous} \def\negquad{\hskip-1em\relax} @@ -553,20 +552,25 @@ \def\sfcc{$\sigma$-finite-cc} \def\sgn{\mathop{\text{sgn}}} \def\shr{\mathop{\text{shr}}\nolimits} +\def\Sint{\mathchoice{\hbox to 0pt{\hskip 3.1pt S\hss}} %unchecked + {\raise 0.6pt\hbox to 0pt{\hskip 3.0pt{\sevenrm S}\hss}} + {\raise 0.4pt\hbox to 0pt{\hskip 1.5pt{\fiverm S}\hss}} %unchecked + {\raise 0.4pt\hbox to 0pt{\hskip 1.5pt{\fiverm S}\hss}} %unchecked + \intop\nolimits} \def\spread{\mathop{\text{spr}}} \def\ssplrarrow{^{\scriptscriptstyle\leftrightarrow}} \def\ssptilde{{\raise1.2ex\hbox{$\scriptscriptstyle\sim$}}} %\def\sspvec{{\raise1.2ex\hbox{$\scriptscriptstyle\rightarrow$}}} \def\sspvec{\mskip3mu\vec{\null}\mskip5mu} -\def\Sti{\mathop{\text{Sti}}} +\def\Sti{\mathop{\text{Sti}}\nolimits} \def\strprime{\,\pmb{\prime}} \def\supp{\mathop{\text{supp}}} \def\tensorhat{\widehat{\otimes}} \def\Tensorhat{\widehat{\bigotimes}} \def\tensorhatsigma{\widehat{\otimes}_{\sigma}} \def\Tr{\mathop{\text{Tr}}} -\def\trs{^{\top}\hskip-1pt} \def\triplepc#1#2#3{(#1,#2,\hbox{$<$}#3)} +\def\TSi{\frak T_{\text{S-i}}} \def\undphi{\underline{\phi}{}} \def\undpsi{\underline{\psi}{}} \def\undtheta{\underline{\theta}{}} @@ -616,7 +620,7 @@ \def\weight{\mathop{\text{wt}}} \def\w1lim{\mathop{\text{w1lim}}} \def\wsid{weakly $(\sigma,\infty)$-{\vthsp}distributive} -\def\1lim{\mathop{\text{1lim}}} +\def\1lim{\mathop{1\mskip-1.5mu\text{lim}}} \def\2vm{two-{\vthsp}valued-{\vthsp}measurable} %Cara\-th\'e\-o\-dory diff --git a/mt04I.tex b/mt04I.tex index 0daa434..13151a8 100644 --- a/mt04I.tex +++ b/mt04I.tex @@ -319,8 +319,8 @@ \section{459}{Symmetric measures and exchangeable random spaces disintegrate into product measures; symmetric quasi-Radon measures; other actions of symmetric groups.} -% \wheader{}{10}{4}{4}{20pt} +\wheader{}{10}{4}{4}{20pt} -% Concordance to Part I \pagereference{576}{} +Concordance to Part I \pagereference{576}{} %577 pages diff --git a/mt04II.tex b/mt04II.tex index a851d8a..faa111b 100644 --- a/mt04II.tex +++ b/mt04II.tex @@ -1,26 +1,26 @@ Chapter 46: Pointwise compact sets of measurable functions -\chapintrosection{15.12.00}{576}{} +\chapintrosection{15.12.00}{8}{} -\section{461}{Barycenters and Choquet's theorem}{9.7.08}{576}{} +\section{461}{Barycenters and Choquet's theorem}{9.7.08}{8}{} {Barycenters; elementary properties; sufficient conditions for existence; closed convex hulls of compact sets; \Krein's theorem; existence and uniqueness of measures on sets of extreme points; ergodic functions and extreme measures.} \section{462}{Pointwise compact sets of continuous -functions}{30.6.07}{588}{} +functions}{30.6.07}{20}{} {Angelic spaces; the topology of pointwise convergence on $C(X)$; weak convergence and weakly compact sets in $C_0(X)$; Radon measures on $C(X)$; separately continuous functions; convex hulls.} -\section{463}{$\frak{T}_p$ and $\frak{T}_m$}{1.2.13}{594}{} +\section{463}{$\frak{T}_p$ and $\frak{T}_m$}{1.2.13}{26}{} {Pointwise convergence and convergence in measure on spaces of measurable functions; compact and sequentially compact sets; perfect measures and Fremlin's Alternative; separately continuous functions.} -\section{464}{Talagrand's measure}{25.5.13}{604}{} +\section{464}{Talagrand's measure}{25.5.13}{36}{} {The usual measure on $\Cal{P}I$; the intersection of a sequence of non-measurable filters; Talagrand's measure; the $L$-space of additive functionals on @@ -28,7 +28,7 @@ \section{464}{Talagrand's measure}{25.5.13}{604}{} \ifdim\pagewidth>467pt\fontdimen3\tenrm=2pt\fi -\section{465}{Stable sets}{28.1.06}{616}{} +\section{465}{Stable sets}{28.1.06}{48}{} {Stable sets of functions; elementary properties; pointwise compactness; pointwise convergence and convergence in measure; a law of large numbers; stable sets and uniform convergence in the strong law @@ -36,13 +36,13 @@ \section{465}{Stable sets}{28.1.06}{616}{} stable sets in $L^0$ and $L^1$; *R-stable sets.} \fontdimen3\tenrm=1.67pt -\section{466}{Measures on linear topological spaces}{2.8.13}{644}{} +\section{466}{Measures on linear topological spaces}{2.8.13}{76}{} {Quasi-Radon measures for weak and strong topologies; Kadec norms; constructing weak-Borel measures; characteristic functions of measures on locally convex spaces; universally measurable linear operators; Gaussian measures on linear topological spaces.} -\section{*467}{Locally uniformly rotund norms}{13.1.10}{653}{} +\section{*467}{Locally uniformly rotund norms}{13.1.10}{85}{} {Locally uniformly rotund norms; separable normed spaces; long sequences of projections; K-countably determined spaces; weakly compactly generated spaces; Banach lattices with @@ -52,23 +52,23 @@ \section{*467}{Locally uniformly rotund norms}{13.1.10}{653}{} Chapter 47: Geometric measure theory -\chapintrosection{25.9.04}{665}{} +\chapintrosection{25.9.04}{97}{} -\section{471}{Hausdorff measures}{23.1.06}{665}{} +\section{471}{Hausdorff measures}{23.1.06}{97}{} {Metric outer measures; Increasing Sets Lemma; analytic spaces; inner regularity; Vitali's theorem and a density theorem; Howroyd's theorem.} -\section{472}{Besicovitch's Density Theorem}{22.3.11}{681}{} +\section{472}{Besicovitch's Density Theorem}{22.3.11}{113}{} {Besicovitch's Covering Lemma; Besicovitch's Density Theorem; *a maximal theorem.} -\section{473}{Poincar\'e's inequality}{25.7.11}{688}{} +\section{473}{Poincar\'e's inequality}{25.7.11}{120}{} {Differentiable and Lipschitz functions; smoothing by convolution; the Gagliardo-\vthsp{}Nirenberg-\vthsp{}Sobolev inequality; Poin\discretionary{-}{}{}car\'e's inequality for balls.} -\section{474}{The distributional perimeter}{17.11.12}{700}{} +\section{474}{The distributional perimeter}{17.11.12}{132}{} {The divergence of a vector field; sets with locally finite perimeter, perimeter measures and outward-normal functions; the reduced boundary; invariance under isometries; isoperimetric inequalities; Federer @@ -76,7 +76,7 @@ \section{474}{The distributional perimeter}{17.11.12}{700}{} \ifdim\pagewidth>467pt\fontdimen3\tenrm=2pt\fi -\section{475}{The essential boundary}{24.1.13}{721}{} +\section{475}{The essential boundary}{24.1.13}{153}{} {Essential interior, closure and boundary; the reduced boundary, the essential boundary and perimeter measures; characterizing sets with locally finite perimeter; @@ -87,13 +87,13 @@ \section{475}{The essential boundary}{24.1.13}{721}{} \fontdimen3\tenrm=1.67pt -\section{476}{Concentration of measure}{10.11.07}{744}{} +\section{476}{Concentration of measure}{10.11.07}{176}{} {Vietoris and Fell topologies; concentration by partial reflection; concentration of measure in $\eightBbb{R}^r$; the Isoperimetric Theorem; concentration of measure on spheres.} -\section{477}{Brownian motion}{2.1.10}{753}{} +\section{477}{Brownian motion}{2.1.10}{185}{} {Brownian motion as a stochastic process; Wiener measure on $C(\coint{0,\infty})_0$; *as a limit of random walks; Brownian motion in $\eightBbb{R}^r$; invariant @@ -103,7 +103,7 @@ \section{477}{Brownian motion}{2.1.10}{753}{} Brownian path is nowhere differentiable; almost every Brownian path has zero two-dimensional Hausdorff measure.} -\section{478}{Harmonic functions}{4.6.09}{778}{} +\section{478}{Harmonic functions}{4.6.09}{210}{} {Harmonic and superharmonic functions; a maximal principle; $f$ is superharmonic iff $\nabla^2f\le0$; the Poisson kernel and harmonic functions @@ -113,7 +113,7 @@ \section{478}{Harmonic functions}{4.6.09}{778}{} harmonic measures and Dirichlet's problem; disintegrating harmonic measures over intermediate boundaries; hitting probabilities.} -\section{479}{Newtonian capacity}{15.2.10}{803}{} +\section{479}{Newtonian capacity}{15.2.10}{235}{} {Defining Newtonian capacity from Brownian hitting probabilities, and equilibrium measures from harmonic measures; submodularity and sequential order-continuity; @@ -134,9 +134,9 @@ \section{479}{Newtonian capacity}{15.2.10}{803}{} Chapter 48: Gauge integrals -\chapintrosection{9.5.11}{845}{} +\chapintrosection{9.5.11}{277}{} -\section{481}{Tagged partitions}{4.9.09}{845}{} +\section{481}{Tagged partitions}{4.9.09}{277}{} {Tagged partitions and Riemann sums; gauge integrals; gauges; residual sets; subdivisions; examples (the Riemann integral, the Henstock integral, the symmetric Riemann-complete integral, the McShane @@ -145,7 +145,7 @@ \section{481}{Tagged partitions}{4.9.09}{845}{} \ifdim\pagewidth>467pt\fontdimen3\tenrm=2pt\fi -\section{482}{General theory}{11.5.10}{855}{} +\section{482}{General theory}{11.5.10}{287}{} {Saks-Henstock lemma; when gauge-{\vthsp}integrable functions are measurable; when integrable functions are gauge-integrable; $I_{\nu}(f\times{\chi}H)$; improper integrals; @@ -153,12 +153,12 @@ \section{482}{General theory}{11.5.10}{855}{} \fontdimen3\tenrm=1.67pt -\section{483}{The Henstock integral}{6.9.10}{869}{} +\section{483}{The Henstock integral}{6.9.10}{301}{} {The Henstock and Lebesgue integrals; indefinite Henstock integrals; Saks-Henstock lemma; Fundamental Theorem of Calculus; the Perron integral; $\|f\|_H$ and $HL^1$; AC$_*$ and ACG$_*$ functions.} -\section{484}{The Pfeffer integral}{21.1.10}{885}{} +\section{484}{The Pfeffer integral}{21.1.10}{317}{} {The Tamanini-Giacomelli theorem; %or Congedo-Tamanini a family of tagged-partition structures; the Pfeffer integral; the @@ -171,52 +171,52 @@ \section{484}{The Pfeffer integral}{21.1.10}{885}{} Chapter 49: Further topics -\chapintrosection{27.9.02}{903}{} +\chapintrosection{27.9.02}{335}{} -\section{491}{Equidistributed sequences}{14.8.08}{903}{} +\section{491}{Equidistributed sequences}{14.8.08}{335}{} {The asymptotic density ideal $\Cal{Z}$; equidistributed sequences; when equidistributed sequences exist; $\frak{Z}=\Cal{P}\eightBbb{N}/\Cal{Z}$; effectively regular measures; equidistributed sequences and induced embeddings of measure algebras in $\frak{Z}$.} -\section{492}{Combinatorial concentration of measure}{30.12.06}{921}{} +\section{492}{Combinatorial concentration of measure}{30.12.06}{353}{} {The Hamming metric; concentration of measure in product spaces; concentration of measure in permutation groups.} -\section{493}{Extremely amenable groups}{4.1.13}{928}{} +\section{493}{Extremely amenable groups}{4.1.13}{360}{} {Extremely amenable groups; concentrating additive functionals; measure algebras under $\Bsymmdiff$; $L^0$; isometry groups of spheres in inner product spaces; locally compact groups.} \section{494}{Groups of measure-preserving automorphisms} -{17.5.13}{936}{} +{17.5.13}{368}{} {Weak and uniform topologies on $\AmuA$; a weakly mixing automorphism which is not mixing; full subgroups and fixed-point subalgebras; extreme amenability; automatic continuity; algebraic cofinality.} -\section{495}{Poisson point processes}{20.12.08}{967}{} +\section{495}{Poisson point processes}{20.12.08}{399}{} {Poisson distributions; Poisson point processes; disintegrations; transforming disjointness into stochastic independence; representing Poisson point processes by Radon measures; exponential distributions and Poisson point processes on $\coint{0,\infty}$.} -\section{496}{Maharam submeasures}{27.5.09}{989}{} +\section{496}{Maharam submeasures}{27.5.09}{421}{} {Submeasures; totally finite Radon submeasures; Souslin's operation; (K-)analytic spaces; product submeasures.} -\section{497}{Tao's proof of Szemer\'edi's theorem}{7.12.10}{998}{} +\section{497}{Tao's proof of Szemer\'edi's theorem}{7.12.10}{430}{} {$\Tau$-removable intersections; and relative independence; permutation-invariant measures on $\Cal{P}([I]^{<\omega})$; and $\Tau$-removable intersections; the Hypergraph Removal Lemma; Szemer\'edi's theorem; a multiple recurrence theorem.} -\section{498}{Cubes in product spaces}{4.9.08}{1010}{} +\section{498}{Cubes in product spaces}{4.9.08}{442}{} {Subsets of measure algebras with non-zero infima; product sets included in given sets of positive measure.} @@ -224,15 +224,15 @@ \section{498}{Cubes in product spaces}{4.9.08}{1010}{} Appendix to Volume 4 -\chapintrosection{3.9.13}{1013}{} +\chapintrosection{3.9.13}{445}{} -\section{4A1}{Set theory}{27.1.13}{1013}{} +\section{4A1}{Set theory}{27.1.13}{445}{} {Cardinals; closed cofinal sets and stationary sets; $\Delta$-system lemma; free sets; Ramsey's theorem; the Marriage Lemma again; filters; normal ultrafilters; Ostaszewski's $\clubsuit$; the size of $\sigma$-algebras.} -\section{4A2}{General topology}{21.4.13}{1017}{} +\section{4A2}{General topology}{21.4.13}{449}{} {Glossary; general constructions; F$_{\sigma}$, G$_{\delta}$, zero and cozero sets; weight; countable chain condition; separation axioms; compact and locally compact spaces; Lindel\"of @@ -243,45 +243,45 @@ \section{4A2}{General topology}{21.4.13}{1017}{} metrizable spaces; Polish spaces; order topologies; Vietoris and Fell topologies.} -\section{4A3}{Topological $\sigma$-algebras}{11.10.07}{1040}{} +\section{4A3}{Topological $\sigma$-algebras}{11.10.07}{472}{} {Borel $\sigma$-algebras; measurable functions; hereditarily Lindel\"of spaces; second-countable spaces; Polish spaces; $\omega_1$; Baire $\sigma$-algebras; product spaces; compact spaces; Baire-property algebras; cylindrical $\sigma$-algebras; spaces of \cadlag{} functions.} -\section{4A4}{Locally convex spaces}{19.6.13}{1050}{} +\section{4A4}{Locally convex spaces}{19.6.13}{482}{} {Linear topological spaces; locally convex spaces; Hahn-Banach theorem; normed spaces; inner product spaces; max-flow min-cut theorem.} -\section{4A5}{Topological groups}{4.8.13}{1056}{} +\section{4A5}{Topological groups}{4.8.13}{488}{} {Group actions; topological groups; uniformities; quotient groups; metrizable groups.} -\section{4A6}{Banach algebras}{8.12.10}{1063}{} +\section{4A6}{Banach algebras}{8.12.10}{495}{} {Stone-Weierstrass theorem (fourth form); multiplicative linear functionals; spectral radius; invertible elements; exponentiation; Arens multiplication.} -\section{4A7}{`Later editions only'}{5.10.13}{1067}{} +\section{4A7}{`Later editions only'}{5.10.13}{499}{} {Items recently interpolated into other volumes.} \wheader{}{10}{2}{2}{100pt} -% Concordance to Part II \pagereference{499}{} +Concordance to Part II \pagereference{499}{} \medskip -References for Volume 4 \vtmpb{3.9.03}\pagereference{1068}{} +References for Volume 4 \vtmpb{3.9.03}\pagereference{500}{} \medskip Index to Volumes 1-4 -\qquad Principal topics and results \pagereference{1075}{} +\qquad Principal topics and results \pagereference{507}{} -\qquad General index \pagereference{1087}{} +\qquad General index \pagereference{519}{} %573 pages diff --git a/mt40I.tex b/mt40I.tex index cbb271c..6c5f7b3 100644 --- a/mt40I.tex +++ b/mt40I.tex @@ -15,7 +15,7 @@ \bigskip -% \centerline{\fourteenbf Part I} +\centerline{\fourteenbf Part I} \vskip 2truein @@ -79,7 +79,7 @@ \bigskip\bigskip -% \centerline{\twentyrm Part I} +\centerline{\twentyrm Part I} \vskip 1truein \vfill @@ -162,7 +162,7 @@ \medskip -% \centerline{\bf Part I} +\centerline{\bf Part I} \bigskip @@ -172,7 +172,7 @@ \wheader{}{10}{4}{4}{120pt} -% \centerline{\bf Part II} +\centerline{\bf Part II} \medskip diff --git a/mti.tex b/mti.tex index 2854218..86afc3a 100644 --- a/mti.tex +++ b/mti.tex @@ -118,7 +118,7 @@ \vfive{----- of null ideals in $\{0,1\}^{\kappa}$ 523E}%5 -\vfive{----- of null ideals in Radon measure spaces 524J, 524P}%5 +\vfive{----- of null ideals in Radon measure spaces 524J, 524Q}%5 \indexivheader{almost} @@ -180,7 +180,7 @@ }%3 \vthree{----- of measure algebras \S383, \S385, \S386, \S387, \S388\vfour{, - 493H, \S494}%4 + \S494}%4 }%3 \indexmedskip%!B @@ -291,7 +291,7 @@ \vfive{Borel liftings \S535}%5 -\vfour{Borel measurable group actions 448S}%4 +\vfour{Borel measurable group actions 448P, 448S}%4 \vfour{Borel measures \S434}%4 @@ -342,8 +342,8 @@ Cantor set and function 134G, 134H \indexivheader{capacity} -\vfour{capacity (Choquet capacity) 432K; (Newtonian capacity, -Choquet-Newton capacity) \S479}%4 +\vfour{capacity (Choquet capacity) 432J {\it et seq.}; +(Newtonian capacity, Choquet-Newton capacity) \S479}%4 \indexheader{\Caratheodory} \Caratheodory's construction of measures from outer measures 113C @@ -393,7 +393,8 @@ \vtwo{----- finding $J$ 235M; }%2 -\vtwo{----- ----- $J=|\det T|$ for linear operators $T$ 263A; $J=|\det\phi'|$ for differentiable operators $\phi$ 263D +\vtwo{----- ----- $J=|\det T|$ for linear operators $T$ 263A; +$J=|\det\phi'|$ for differentiable operators $\phi$ 263D }%2 \vtwo{----- ----- ----- when the measures are Hausdorff measures 265B, 265E @@ -433,7 +434,7 @@ \indexvheader{codable} \vfive{codable Borel sets \S562}%5 -\vfive{----- ----- functions 562K +\vfive{----- ----- functions 562M }%5 \vfive{\indexheader{cofinality}} @@ -443,7 +444,7 @@ \vfive{----- of null ideals in $\{0,1\}^{\kappa}$ 523N}%5 -\vfive{----- of null ideals in Radon measure spaces 524J, 524P}%5 +\vfive{----- of null ideals in Radon measure spaces 524J, 524Q}%5 \vfive{----- of reduced products 5A2B, 5A2C}%5 @@ -493,6 +494,9 @@ \vtwo{----- product measures 251C, 251F, 251W, 254C}%2 +\vthree{----- of invariant measures 395P\vfour{, + 441C, 441E, 441H, 448P}}%3%4 + \vfour{----- from inner measures 413C}%4 \vfour{----- extending given functionals or measures @@ -526,8 +530,6 @@ \vfour{----- ----- yielding Radon measures (Riesz' theorem) 436J, 436K }%4 -\vfour{----- of invariant measures 441C, 441E, 441H, 448P}%4 - \vfour{----- from conditional distributions 455A, 455C, 455E, 455G, 455P}%4 @@ -618,7 +620,7 @@ \vfive{----- of null ideals in $\{0,1\}^{\kappa}$ 523G}%5 -\vfive{----- of null ideals in Radon measure spaces 524J, 524P}%5 +\vfive{----- of null ideals in Radon measure spaces 524J, 524Q}%5 \vtwo{\indexmedskip}%!D @@ -818,6 +820,7 @@ \vtwo{----- converge a.e.\ for square-integrable function 286V}%2 +\wheader{Fourier}{0}{0}{0}{36pt} \vtwo{Fourier transforms}%2 \vtwo{----- on $\Bbb R$ \S283, \S284}%2 @@ -1143,7 +1146,7 @@ \indexmedskip%!L -\indexheader{Lebesgue} +\indexheader{Lebesgue's Density Theorem} \vtwo{Lebesgue's Density Theorem (in $\Bbb R$) \S223}%2 \vtwo{----- $\lim_{h\downarrow 0}\bover1{2h}\int_{x-h}^{x+h}f=f(x)$ a.e.\ @@ -1301,7 +1304,7 @@ \vfour{----- with \cadlag\ sample paths 455G}%4 -\vfour{----- Markov property 455C; strong Markov property 455O, 455T}%4 +\vfour{----- Markov property 455C; strong Markov property 455O, 455U}%4 \vfour{----- {\it see also} L\'evy process, Brownian motion}%4 @@ -1332,6 +1335,8 @@ \vtwo{----- existence 213L}%2 +\wheader{measurable}{0}{0}{0}{36pt} + measurable functions ----- (real-valued) \S121 @@ -1426,7 +1431,8 @@ \vthree{----- characterizations 395D\vfour{, 448D}%4 }%3 -\vthree{----- and invariant functionals 395O, 395P, 396B\vfour{, 448P}%4 +\vthree{----- and invariant functionals 395O, 395P, 396B\vfour{, +448P, 449L}%4 }%3 \indexvheader{normal} @@ -1459,7 +1465,8 @@ \vtwo{ordering of measures 234P}%2 \indexheader{Ornstein} -\vthree{Ornstein's theorem (on isomorphism of Bernoulli shifts with the same entropy) 387I, 387K +\vthree{Ornstein's theorem +(on isomorphism of Bernoulli shifts with the same entropy) 387I, 387K }%3 \indexheader{outer} @@ -1479,7 +1486,7 @@ \vthree{perfect measure space 342K {\it et seq.}\vfour{, \S451}%4 }%3 -\vfour{----- and pointwise compact sets of measurable functions 463J +\vfour{----- and pointwise compact sets of measurable functions 463K }%4 \vfour{\indexheader{perimeter}} @@ -1526,7 +1533,7 @@ \vfive{----- and saturation of products 516T}%5 -\vfive{----- of measurable algebras 525D, 525J-525Q +\vfive{----- of measurable algebras 525C, 525I-525P }%5 \indexiiheader{product} @@ -1620,7 +1627,7 @@ \vfour{----- products 415E, 417N, 417O}%4 -\vfour{----- on locally convex spaces \S466}%4 +\vfour{----- on locally convex spaces 466A}%4 \vtwo{\indexmedskip}%!R @@ -1663,10 +1670,10 @@ \vfour{----- Haar measures 441E; other invariant measures 441H, 448P}%4 -\vfour{----- on locally convex spaces \S466 +\vfour{----- on locally convex spaces 466A }%4 Radon measures -\vfive{----- cardinal functions 524J, 524P}%5 +\vfive{----- cardinal functions 524J, 524Q}%5 \vtwo{Radon-Nikod\'ym theorem (truly continuous additive set-functions have densities) 232E @@ -1744,7 +1751,7 @@ }%4 \indexvheader{resolvable} -\vfive{resolvable sets and functions are self-coding 562G, 562P +\vfive{resolvable sets and functions are self-coding 562I, 562R }%5 \indexiiiheader{Riesz} @@ -1772,7 +1779,9 @@ \vfive{saturated ideal of sets \S541}%5 \indexiiiheader{Shannon} -\vthree{Shannon-McMillan-Breiman theorem (entropy functions of partitions generated by a measure-preserving homomorphism converge a.e.) 386E}%3 +\vthree{Shannon-McMillan-Breiman theorem +(entropy functions of partitions generated by a measure-preserving +homomorphism converge a.e.) 386E}%3 \indexvheader{Shelah} \vfive{Shelah four-cardinal covering number 5A2G}%5 @@ -1916,7 +1925,7 @@ \vtwo{surface measure in $\BbbR^r$ \S265}%2 \vfour{\indexheader{symmetric}} -\vfour{symmetric group 449Xg, 492H, 493Xb +\vfour{symmetric group 449Xh, 492H, 493Xb }%4 \indexivheader{Szemer\'edi} @@ -1983,7 +1992,7 @@ \vfive{----- of null ideals in $\{0,1\}^{\kappa}$ 523H-523L}%5 -\vfive{----- of null ideals in Radon measure spaces 524J, 524P}%5 +\vfive{----- of null ideals in Radon measure spaces 524J, 524Q}%5 \indexiiheader{uniformly} \vthree{uniformly exhaustive submeasures}%3 @@ -2046,6 +2055,7 @@ \vfour{weakly compactly generated normed spaces 467L }%4 +\wheader{weakly}{0}{0}{0}{36pt} \vthree{weakly $(\sigma,\infty)$-distributive Boolean algebras 316G {\it et seq.}}%3 @@ -2211,6 +2221,7 @@ %\indexheader{$\scriptstyle\pmb{R}$} \indexiiiheader{$\scriptstyle\pmb{S}$} +%\indexiiiheader{$\scriptstyle\pmb{S}(\frak A)$} \vthree{$S(\frak A)$ (space of `simple' functions corresponding to a Boolean ring $\frak A$) \S361}%3 @@ -2304,7 +2315,7 @@ \vfour{\indexheader{abelian}} \vfour{abelian topological group 441Ia, 444D, 444Og, {\it 444Sb}, 444Xd, -444Xk, \S445, 446Xb, 449Cf, 455Xk, 461Xk, 491Xm +444Xk, \S445, 446Xa, 449Cf, 455Xk, 461Xk, 491Xm }%4 \indexiiheader{absolute} @@ -2326,9 +2337,9 @@ 225C-225G, %225C 225D 225E 225F 225G 225K-225O, %225K 225L 225M {\it 225N} 225O 225Xa-225Xh, %225Xa 225Xb 225Xc 225Xd 225Xe 225Xf 225Xg 225Xh -225Xn, 225Xo, 225Ya, 225Yc, {\it 232Xb}, {\it 233Xc}, {\it 244Yi}, -252Ye, 256Xg, 262Bc, 263I, {\bf 264Yp}, 265Ya, {\it 274Xb}, 282R, 282Yf, -{\it 283Ci}\vfive{, +225Xn, 225Ya, 225Yc, 225Yg, {\it 232Xb}, {\it 233Xc}, {\it 244Yi}, +252Ye, 256Xg, 262Bc, 263J, {\bf 264Yp}, 265Ya, {\it 274Xb}, 282R, 282Yf, +{\it 283Ci}, {\it 283Ya}, {\it 283Yb}\vfive{, 565M}%5 }%2 absolutely continuous function @@ -2348,25 +2359,25 @@ %Ac \indexivheader{action} -\vfour{action of a group on a set 394Na, 425C-425E, %425C 425D 425E +\vfour{action of a group on a set 394Na, 425B-425E, %425B 425C 425D 425E 425Xf, 425Xg, 425Ya, 425Yb, 425Za, 441A, 441C, 441K, 441L, 441Xa-441Xc, %441Xa 441Xb 441Xc 441Xt, 441Ya, 441Yf, 441Yl-441Ym, %441Yl 441Ym 441Yn -441Yp, 442Xe, 443Yt, -448Xi, 449L, 449N, 449Xo, 449Ye, 449Yg, 449Yh, 459I, 459J +441Yp, 442Xe, 443Ye, +448Xh, 449L, 449N, 449Xp, 449Ye, 449Yg, 449Yh, 459I, 459J 497F, {\bf 4A5B}, 4A5C\vfive{, 535Yd}%5 }%4 -\vfour{----- Borel measurable action 424H, 425Bb, 448P, 448S, 448T, 448Xf, +\vfour{----- Borel measurable action 424H, 425Bb, 448P, 448S, 448T, 448Xe, {\bf 4A5I} }%4 \vfour{----- continuous action 424H, {\it 441B}, 441Ga, {\it 441L}, 441Xa, 441Xn, 441Xo, 441Xt, 441Yf, 441Yk, 441Yo, 441Yq, 443C, 443G, 443P-443R, %443P 443Q 443R -443U, 443Xd, 443Yc, 443Yu, 444F, 448T, 449A, 449B, 449D, +443U, 443Xd, 443Yc, 443Yf, 444F, 448T, 449A, 449B, 449D, 452T, 455Xf, 461Yf, 461Yg, 497Xb, {\bf 4A5I}, 4A5J }%4 @@ -2401,14 +2412,14 @@ completely additive ({\bf 326N}) }%3 -\vfour{additive\vfive{ (in `$\kappa$-additive ideal') {\bf 511F}; - (in `$\kappa$-additive measure') {\bf 511G}; }%5 +\vfour{additive\vfive{ (in `$\kappa$-additive ideal') {\bf 511Fa}; + (in `$\kappa$-additive measure') {\bf 511Ga}; }%5 {\it see also} $\tau$-additive ({\bf 411C}) }%4 \vfive{\indexheader{additivity}} \vfive{additivity of a pre- or partially ordered set -{\bf 511Bb}, 511F, 511Hg, 511Xa, 511Xk, +{\bf 511Bb}, 511Fa, 511Hg, 511Xa, 511Xm, 512Ea, 513Ca, 513E, 513Ga, 513I, 513Xb, 513Xf, {\it 514Xj}, 518Bc, 522Yc, 527Xh, {\it 542J}, 5A2A, 5A2Ba }%5 @@ -2422,17 +2433,17 @@ 546O, 555Bb, 555Q, 555Ya, 555Yb, 5A1Ab }%5 -\vfive{----- of a null ideal 511Xc-511Xe, %511Xc 511Xd 511Xe +\vfive{----- of a null ideal 511Xd-511Xf, %511Xd 511Xe 511Xf 521A, 521D-521F, %521D 521E 521Fb -521H, 521I, 521Ya, 522V, 523B, 523E, 523P, 523Xd, 524I, 524Ja, 524Pa, -524R-524T, %524R 524S 524Ta +521H, 521I, 521Ya, 522V, 523B, 523E, 523P, 523Xd, 524I, 524Ja, 524Qa, +524S-524U, %524S 524T 524Ua 524Xj, 524Xk, 524Zb, 533A, 533B, 536Xa, 537Ba, 537Xh, 544K, 544Ya, 552F }%5 additivity of a null ideal -\vfive{----- of a measure {\bf 511G}, 511Xc-511Xe, %511Xc 511Xd 511Xe +\vfive{----- of a measure {\bf 511Ga}, 511Xd-511Xf, %511Xd 511Xe 511Xf 521A, 521B, 521D-521F, %521Dc 521E 521F 521K, 521Xa, 521Xk, 523E, 523P, -524Ja, 524Pa, 524Ta, 528Xe, 534B, 535H, +524Ja, 524Qa, 524Ua, 528Xe, 534B, 535H, 543A-543C, %543Aa 543Ba 543C 543F-543H, %543F 543G 543H 544I, 544Za, 545A @@ -2441,7 +2452,7 @@ \vfive{----- of Lebesgue measure {\it 419A}, 521I, 522B, 522E, 522F, 522P, 522S-522V, %522S 522Tc 522U 522Va -522Ya, 523G, 524Mb, 524Pa, 524Ta, 525Xc, 526G, +522Ya, 523G, 524Mb, 524Qa, 524Ua, 525Xc, 526G, 528L-528O, %528L 528M 528N 528O 529F, 529Xc-529Xe, %529Xc 529Xd 529Xe 529Xg, 529Yc, @@ -2470,7 +2481,7 @@ \vfour{affine subspace {\it 476Xf} }%4 -\vfour{affine transformation 443Yr +\vfour{affine transformation 443Yt }%4 %Ag%Ah%Ai%Aj%Ak%Al @@ -2493,7 +2504,7 @@ {\bf 231A}, 231B, 231Xa\vthree{, 311Bb, 311Xb, 311Xh, 312B, 315G, 315M, 362Xg, 363Ye, 381Xa\vfour{, 475Ma, 4A3Cg\vfive{, - 541C, 562Ag, 562F, 562Rb}}}}; %2%3%4%5 + 541C, 562Bd, 562H, 562Tb}}}}; %2%3%4%5 % alg of sets {\it see also }\vthree{Boolean algebra ({\bf 311A}),} $\sigma$-algebra ({\bf 111A}) @@ -2563,11 +2574,10 @@ 449E-449G, %449E 449F {\it 449G}, 449J, 449K, 449M, 449N 449Xa-449Xd, %449Xa 449Xb 449Xc 449Xd -449Xg-449Xp, - %449Xg 449Xh 449Xi 449Xj 449Xk 449Xl 449Xm 449Xn 449Xo 449Xp -449Yd, 449Yf, -{\it 449Yi}, 449Yk, 461Yf, 461Yg, 493Ya, -494J-494L; % 494J, 494K, 494L +449Xh-449Xq, + %449Xh 449Xi 449Xj 449Xk 449Xl 449Xm 449Xn 449Xo 449Xp 449Xq +449Yf, {\it 449Yi}, 461Yf, 461Yg, 493Ya, +494J-494L; %494J, 494K, 494L {\it see also} extremely amenable ({\bf 493A}) }%4 }%3 @@ -2602,7 +2612,7 @@ {\it 479B-479E}, %{\it 479B 479Cb 479D 479E} {\it 479M-479P}, %{\it 479M 479N 479O {\it 479Pa}} {\it 479Xf}, {\it 479Yc}, 498A, 496K\vfive{, - 513Ob, 513Yf, {\it 522Va}, 534Bd, 562E, 562Ya, 563I, 567Xp}; + 513Ob, 513Yf, {\it 522Va}, 534Bd, 562F, 562Yb, 563I, 567Xp}; {\it see also} K-analytic ({\bf 422F}) }%4 analytic top sp @@ -2650,6 +2660,10 @@ }%2 % Arch R sp +\indexiiheader{Archimedes} +\vtwo{Archimedes 265Xf +} + \indexiiheader{area} \vtwo{area {\it see} surface measure }%2 @@ -2751,16 +2765,15 @@ 375B, 375Xb, 375Yc, 381P, 382P, 384E, 384F, 384Xb, 386D, 386M, {\it 387Cd}, {\it 387C-387H}, %{\it 387C 387D 387E 387F 387G 387H} -{\it 387L}, 393Yi\vfour{, - 494E\vfive{, - 515Ya, 539E, {\it 539H}, 541P, 546Ce, 546H, 546M}}; %4%5 +{\it 387L}, 393Yi\vfive{, + 515Ya, 539E, {\it 539H}, 541P, 546Ce, 546H, 546M}; %5 {\it see also} relatively atomless ({\bf 331A}) }%3 atomless B alg \vthree{atomless measure algebra 322Bg, 322Lc, 331C, 369Xh, 374Xl, 377C, 383G, 383H, 383J, 383Xg, 383Xh, {\it 383Ya}, 384Ld, 384M, 384O, 384P, {\it 384Xd}\vfour{, - 493D, 493H, 493Ya, 494I, 494R, 494Xg, {\it 494Xi}, 494Xl, + 493D, 493Ya, 494E, 494I, 494R, 494Xg, {\it 494Xi}, 494Xl, 494Yi\vfive{, 528Bb, 528D-528F, %{\it 528D} 528E {\it 528F} 528K, 528N, @@ -2810,10 +2823,10 @@ %Au \indexvheader{augmented} -\vfive{augmented shrinking number (of an ideal) {\bf 511Fb}, 511J -}%5 +\vfive{augmented shrinking number (of an ideal) {\bf 511Fc}, 511J +}%5 \shr^+ -\vfive{----- (of a null ideal) 511Xc-511Xe, %511Xc 511Xd 511Xe +\vfive{----- (of a null ideal) 511Xd-511Xf, %511Xd 511Xe 511Xf 521C-521F, %521Ca 521Dd 521E 521Fb 521Ha, 521I, 521Xc, 523Mb, 523P, 523Xd, 523Ya, 524Xg, 537O-537S %537O 537P 537Q 537R 537S @@ -2847,7 +2860,7 @@ \vthree{----- ----- of a measure algebra {\it 366Xh}, 374J, \S\S383-384, 395F, 395R\vfour{, - 425Yb, 425Zc, 446Yc, 493G, 493H, \S494\vfive{, + 425Yb, 425Zc, 446Yc, \S494\vfive{, 566R, 566Xg-566Xi %566Xg 566Xh 566Xi }}%4%5 }%3 \AmuA @@ -2993,7 +3006,7 @@ }%5 \vfour{Baire measurable function 417Be, 437Yg, {\bf 4A3Ke}\vfive{; - {\it see also} codable Baire function ({\bf 562Rc})}%5 + {\it see also} codable Baire function ({\bf 562Tc})}%5 }%4 \vfour{Baire measure {\bf 411K}, 411Xf, 411Xh, 412D, 415N, 416Xl, 432F, @@ -3012,7 +3025,7 @@ }%3 Baire property \vthree{Baire-property algebra {\bf 314Yd}, 341Yb, 367Yk\vfour{, - 414Xk, 431F, 466Xh, 496G, {\bf 4A3Q}, 4A3R\vfive{, + 414Xk, 431F, 466Xk, 496G, {\bf 4A3Q}, 4A3R\vfive{, 514I, 527D, 527Xd, 527Yc, 551Hc, 551Xc, 567Ec, 567I, 567Xr, 5A4E}}%5%4 }%3 @@ -3022,23 +3035,23 @@ \vfour{Baire set 417Be, 417Xt, 421L, 422Xd, 422Xe, 434Hc, 434Pd, 435H, {\bf 4A3K}, 4A3Yc\vfive{, 5A4Ed; - {\it see also} codable Baire set ({\bf 562R})}%5 + {\it see also} codable Baire set ({\bf 562T})}%5 }%4 \vthree{Baire space {\bf 314Yd}, 341Yb, 364Yj, 364Ym, 367Yi, 367Yk\vfour{, {\bf 4A2A}, 414Xk, 4A3Ra\vfive{, - 514If, 514Jb, 561E, 561Yd, 5A4H}%5 + 514If, 514Jb, 561E}%5 }%4 }%3 -\vthree{Baire's theorem 3A3G\vfour{, 4A2Ma\vfive{, 561E, 561F}}%4%5 +\vthree{Baire's theorem 3A3G\vfour{, 4A2Ma\vfive{, 561E}}%4%5 }%3 \vthree{Baire $\sigma$-algebra 254Xs, {\it 333M}, {\bf 341Yc}, 341Zb, 343Xc, 344E, 344F, 344Yc-344Ye\vfour{, %344Yc, 344Yd, 344Ye 411R, 415Xp, 417U, 417V, 421Xg, 421Yc, 423Db, {\it 434Yn}, 435Xa, 435Xb, -437E, 439A, 443Yh, 449Xl, 452N, 455Ia, 461Xg, 496Ye, +437E, 439A, 443Yi, 449Xm, 452N, 455Ia, 461Xg, 463M, 496Ye, {\bf 4A3K}, 4A3L-4A3P, %4A3L 4A3M 4A3N 4A3O 4A3P 4A3U-4A3W, %4A3U 4A3V 4A3W 4A3Xb-4A3Xd, %4A3Xb 4A3Xc 4A3Xd @@ -3069,7 +3082,7 @@ \indexheader{Banach} \vtwo{Banach algebra $\pmb{>}${\bf 2A4Jb}\vthree{, 363Xa\vfour{, - 444E, 444S, 444Xv, 444Yb, 444Yc, {\it 445H}, 446A, {\bf 4A6Ab}, 4A6F; + 444E, 444S, 444Xv, 444Yb, 444Yc, {\it 445H}, 446Aa, {\bf 4A6Ab}, 4A6F; {\it see also} commutative Banach algebra ({\bf 4A6Aa}), unital Banach algebra ({\bf 4A6Ab}) }%4 @@ -3130,7 +3143,7 @@ \vthree{band algebra (of an Archimedean Riesz space) {\bf 353B}, 353D, 356Yc, 361Yd, 362Ya, 362Yb, 365S, {\it 365Xm}, 366Xb, 368E, 368R, 393Yf\vfive{, - 511Xm}; + 511Xn}; {\it see also} complemented band algebra ({\bf 352Q}), projection band algebra ({\bf 352S}) }%3 @@ -3152,7 +3165,8 @@ }%4 \vthree{base for a topology {\bf 3A3M}\vfour{, - 4A2Ba, 4A2Fc, 4A2Lg, 4A2Ob, 4A2Pa}%4 + 4A2Ba, 4A2Fc, 4A2Lg, 4A2Ob, 4A2Pa\vfive{, + 561Ye}}%4%5 }%3 \vfour{----- {\it see also} $\pi$-base ({\bf 4A2A}) @@ -3233,8 +3247,8 @@ \indexheader{bilateral} \vfour{bilateral uniformity on a topological group 441Xp, 443H, 443I, -443K, 443Xj, 443Ye, 444Xt, {\it 445Ab}, 445E, 445Ya, 449Xh, 493Xa, -494Bc, 494Cf, {\bf 4A5Hb}, 4A5M-4A5O, %4A5M 4A5N 4A5O +443K, 443Xj, 443Yg, 444Xt, {\it 445Ab}, 445E, 445Ya, 449Xi, 493Xa, +494Bd, 494Cf, {\bf 4A5Hb}, 4A5M-4A5O, %4A5M 4A5N 4A5O 4A5Q\vfive{, 534Xk}%5 }%4 @@ -3251,9 +3265,9 @@ %Bj%Bk%Bl -\indexvheader{Blumberg} -\vfive{Blumberg's theorem 5A4H -}%5 +%\indexvheader{Blumberg} +%\vfive{Blumberg's theorem 5{}A4H +%}%5 %Bm%Bn%Boa%Bob%Boc @@ -3271,7 +3285,7 @@ \indexheader{Boolean} \vthree{Boolean algebra chap.\ 31 ({\bf $\pmb{>}$311Ab}), 363Xf\vfive{, - \S556, 561Xn}; %5 + \S556, 561Xq}; %5 {\it see also} algebra of sets, complemented band algebra ({\bf 352Q}), Dedekind ($\sigma$-\nobreak)complete Boolean algebra, Maharam algebra ({\bf 393E}), @@ -3287,7 +3301,7 @@ 382G-382N, %382G 382H 382I 382J 382K 382L 382M 382N 382Xa-382Xc, %382Xa 382Xb 382Xc 382Xk, 382Xl, 384A, 388D, 388Ya, 395Ge, 395Ya, 396A\vfour{, - 425Ac, {\it 442H}, 443Af, 443Yt\vfive{, + 425Ac, {\it 442H}, 443Af, 443Ye\vfive{, 556Cd, 556Jb, 5A6H}}; %4%5 {\it see also}\vfour{ Borel automorphism,} cyclic automorphism ({\bf 381R}), ergodic automorphism, @@ -3366,9 +3380,9 @@ \vtwo{Borel-Cantelli lemma 273K }%2 -\vfive{Borel code (for a set) {\bf 562A}, 562B, 562G; - (for a real-valued function) 562L, 562P; - (for an element in a Boolean algebra) 562T +\vfive{Borel code (for a set) {\bf 562B}, 562C, 562I; + (for a real-valued function) 562N, 562R; + (for an element in a Boolean algebra) 562V }%5 \vfive{Borel-coded measure {\bf 563A}, 563B, 563C, 563F, @@ -3384,7 +3398,7 @@ \vfour{Borel constituent {\it see} constituent ({\bf 423P}) }%4 -\vfive{Borel equivalence {\it see} codable Borel equivalence ({\bf 562Na}) +\vfive{Borel equivalence {\it see} codable Borel equivalence ({\bf 562Pa}) }%5 \vfour{Borel isomorphism 254Xs, @@ -3405,11 +3419,11 @@ {\it 417Bb}, {\it 418Ac}, 423G, 423Ib, 423O, 423Rd, 423Xi, 423Yc, {\it 423Ye}, 433D, 434Xi, 437Jd, 437Yg, 437Yu, 443Jb, {\it 444F}, {\it 444G}, -{\it 444Xg}, 466Xh, 471Xf, 472Xd, 473Ya, {\it 474E}, 474Xa, 476Xa, +{\it 444Xg}, 466Xk, 471Xf, 472Xd, 473Ya, {\it 474E}, 474Xa, 476Xa, 494Xf, {\bf 4A3A}, 4A3C, 4A3Dc, 4A3Gb\vfive{, 513M, 513O, 567Eb, 567Yf, 5A4D}; %5 {\it see also} Borel isomorphism, Borel measurable action\vfive{, - codable Borel function ({\bf 562J})}}}}%5%4%3%2 + codable Borel function ({\bf 562L})}}}}%5%4%3%2 \vtwo{Borel measure\vfour{ {\bf $\pmb{>}$411K}, 411Xf-411Xh, %411Xf 411Xg 411Xh @@ -3452,8 +3466,8 @@ 443Xm, {\it 444F}, {\it 444Xg}, {\it 451O}, {\bf 4A3A}, 4A3G-4A3J, %4A3Gb 4A3H 4A3I 4A3J 4A3Ya\vfive{, - 562Cb; - {\it see also} codable Borel set ({\bf 562Ag})}%5 + 562Db; + {\it see also} codable Borel set ({\bf 562Bd})}%5 }%4 Borel set in other spaces \vfour{Borel space {\it see} standard Borel space ({\bf 424A}) @@ -3465,7 +3479,7 @@ {\it 212Xc}, {\it 212Xd}, {\it 216A}, 251M\vthree{, 364F, 366Yk, 366Yl, 382Yc\vfour{, 439A\vfive{, - 521Xa, 535Ya, 546J, 546Q, 561Xr, 566Ob, 566Xb, 567Xo}}}}; + 521Xa, 535Ya, 546J, 546Q, 561Xd, 566Ob, 566Xb, 567Xo}}}}; ----- (of other spaces) {\bf 135C}, 135Xb\vtwo{, {\bf 256Ye}, 271Ya\vthree{, @@ -3473,9 +3487,9 @@ {\it 411K}, 414Xk, 421H, 421Xd-421Xf, %421Xd 421Xe 421Xf 421Xj, 421Xl, 423N, 423S, 423Xd, 423Yc, 424Xb, 424Xd-424Xf, %424Xd 424Xe 424Xf -424Yb, {\it 431Xa}, 433J, 434Dc, 435Xb, 435Xd, 437H, 443Jb, 443Yi, +424Yb, {\it 431Xa}, 433J, 434Dc, 435Xb, 435Xd, 437H, 443Jb, 443Yj, 448Q, 448R, {\it 449J}, 452N, -477Ha, 461Xi, 466Ea, 466Xn, 466Yc, 466Ye, 466Za, 467Ye, 496J, 496K, +477Ha, 461Xi, 466Ea, 466Xg, 466Yb, 466Za, 467Ye, 496J, 496K, {\bf 4A3A}, 4A3C-4A3G, %4A3C 4A3D 4A3E 4A3F 4A3Ga 4A3Kb, 4A3N, 4A3R, 4A3V, 4A3Wc, 4A3Xa, 4A3Xd\vfive{, 522Vb, 527Xd, 535La, {\it 551Xc}, {\it 551Ya}, @@ -3489,7 +3503,7 @@ \vfour{\indexheader{boundary} boundary of a set in a topological space 411Gi, {\it 437Xj}, 474Xc, -475C, {\it 475Jb}, 475S, 475T, 475Xa, 479B, 479Mc, 479Pc, +475C, {\it 475Jc}, 475S, 475T, 475Xa, 479B, 479Mc, 479Pc, {\bf 4A2A}, 4A2Bi; {\it see also} essential boundary ({\bf 475B}), reduced boundary ({\bf 474G}) @@ -3504,7 +3518,7 @@ 253Yf, 253Yj, {\bf 2A4F}, 2A4G-2A4I, %2A4G 2A4H 2A4I 2A5If\vthree{, 355C, 3A5Ed\vfour{, - 456Xh, 466L, 466M, {\it 466Yb}, 4A4Ib\vfive{, + 456Xh, 466L, 466M, {\it 466Yd}, 4A4Ib\vfive{, 567Ha, 567Xj}}}; %4%3%5 {\it see also} \vthree{(weakly) compact linear operator ({\bf 3A5L}), order-bounded linear operator ({\bf 355A}),}\vfour{ @@ -3526,10 +3540,10 @@ \vtwo{bounded variation, function of \S224 ({\bf 224A}, {\bf 224K}), 225Cb, 225M, {\it 225Oc}, {\it 225Xh}, {\it 225Xn}, 225Yc, 226Bc, 226C, 226Yd, 263Ye, 264Yp, 265Yb, 282M, 282O, 283L, 283Xj, 283Xk, {\it 283Xm}, -{\it 283Xn}, {\it 283Xq}, 284Xk, {\it 284Yd}\vthree{, +{\it 283Xn}, {\it 283Ya}, {\it 283Yb}, 284Xl, {\it 284Yd}\vthree{, 343Yc, 354Xt\vfour{, 437Xc, 438Xs, 438Yh, 483Xg, 483Ye\vfive{, - 562Oc, 565M}}%4%5 + 562Qc, 565M}}%4%5 }%3 }%2 bounded variation @@ -3572,11 +3586,12 @@ \vfour{Brownian exit probability {\bf 477Ia} }%4 -\vfour{Brownian exit time {\bf 477Ia}, 478N, 478O, 478V, 478Xg +\vfour{Brownian exit time {\bf 477Ia}, +478N, 478O, 478V, 478Xg, {\it 479Xt} }%4 -\vfour{Brownian hitting probability {\bf 477I}, {\it 478Pa}, 478U, 478Xe, -478Ye, 478Yj, 478Yk, 479Lc, +\vfour{Brownian hitting probability {\bf 477I}, {\it 478Pa}, 478U, 478Xd, +478Ye, 478Yj, 478Yk, 479Lc, 479Pb, 479Xd, 479Xn, 479Xr; {\it see also} outer Brownian hitting probability ({\bf 477I}) }%4 @@ -3586,7 +3601,7 @@ \vfour{Brownian motion 455Xg, \S477 ({\bf 477A}), 478K, 478M-478P, %478M 478N 478O 478Pc -478Xd +478Xd, 479Xt }%4 \vfour{----- typical path properties 477K, 477L, 477Xh, 477Ye, 477Yi, @@ -3615,9 +3630,9 @@ %Cacciopoli set = finite perimeter, or bounded + finite perimeter -\indexivheader{c\`adl\`ag} -\vfour{c\`adl\`ag function (`continue \`a droit, limite \`a gauche') -{\it 438Yk}, 455Gc, 455H, 455K, 455O, 455Pc, 455S, 455T, 455Yb, 455Ye, +\indexivheader{\cadlag} +\vfour{\cadlag\ function (`continue \`a droit, limite \`a gauche') +{\it 438Yk}, 455Gc, 455H, 455K, 455O, 455Pc, 455Sc, 455U, 455Yb, 455Ye, {\bf 4A2A}, 4A3W }%4 cadlag @@ -3673,7 +3688,8 @@ \Caratheodory's method (of constructing measures) 113C, 113D, 113Xa, 113Xd, 113Xg, 113Yc, 113Yk, 114E, 114Xa, 115E, {\it 121Ye}, 132Xc, 136Ya\vtwo{, - 212A, {\it 212Xf}, 213C, 213Xa, 213Xb, 213Xd, 213Xf, {\it 213Xg}, 213Xj, 213Ya, + 212A, {\it 212Xf}, +213C, 213Xa, {\it 213Xb}, {\it 213Xd}, 213Xf, {\it 213Xg}, 213Xi, 213Yb, 214H, 214Xb, 216Xb, {\it 251C}, {\it 251Wa}, {\it 251Xe}, {\it 264C}, {\it 264K}\vfour{, 413Xd, 413Xm, 431C, {\it 436Xc}, {\it 436Xk}, 452Xi, 471C, 471Ya\vfive{, @@ -3705,7 +3721,6 @@ {\it see also} cardinal power ({\bf 5A1E}) }%5 -\vthree{\indexheader{cardinal function}} \vthree{cardinal function of a Boolean algebra {\it see} cellularity ({\bf 332D}\vfive{, {\bf 511Db}), centering number ({\bf 511De}), Freese-Nation number ({\bf 511Dh}), linking number ({\bf 511D})}, @@ -3717,8 +3732,8 @@ }%3 \vfive{----- ----- of an ideal {\it see} augmented shrinking number -({\bf 511Fb}), covering number ({\bf 511Fc}), -shrinking number ({\bf 511Fb}), uniformity ({\bf 511Fa}) +({\bf 511Fc}), covering number ({\bf 511Fd}), +shrinking number ({\bf 511Fc}), uniformity ({\bf 511Fb}) }%5 \vthree{----- ----- of a measure algebra {\it see} magnitude ({\bf 332Ga}) @@ -3730,7 +3745,7 @@ ({\bf 511B}),}\vfive{ centering number ({\bf 511Bg}),} cofinality ({\bf 3A1F}\vfive{, {\bf 511Ba}})\vfive{, coinitiality ({\bf 511Bc}), Freese-Nation number ({\bf 511Bi}), -linking number ({\bf 511Bf}), Martin number ({\bf 511Bh}), +linking number ({\bf 511B}), Martin number ({\bf 511Bh}), saturation ({\bf 511B})}%5 }%3 @@ -3756,7 +3771,7 @@ }%5 \indexheader{Carleson} -\vtwo{Carleson's theorem 282K {\it remarks}, 282 {\it notes}, 284Yg, +\vtwo{Carleson's theorem 282K {\it remarks}, 282 {\it notes}, {\it 284Yg}, 286U, 286V }%2 @@ -3774,12 +3789,12 @@ carry Haar measures (in `topological group carrying Haar measures') {\bf 442D}, 442Xb, 442Xc, 443A, 443C-443F, %443C 443D 443E 443F -443H, 443J, 443K, 443N, 443Xb, 443Xd, 443Xe, +443H, 443J, 443K, 443N, 443Xb, 443Xd, 443Xh-443Xj, %443Xh, 443Xi, 443Xj, -443Xm, 443Ya, 443Yb, 443Yj, 444J, 444L, +443Xm, 443Ya, 443Yb, 443Yl, 444J, 444L, 444Xi-444Xk, %444Xi 444Xj 444Xk 444Xm, 444Xn, 444Yj, 445J, 445O, 445Xc, 445Yi, 445Yj, 447A, 447B, 447J, -449Yd, 493Xf\vfive{, +449Yd, 493Xh, 494Xb\vfive{, 531Xf}; %5 {\it see also} Haar measure }%4 @@ -3802,7 +3817,7 @@ \vtwo{Cauchy filter {\bf 2A5F}, 2A5G\vthree{, 354Ec, {\bf 3A4F}\vfour{, - 4A2Jh}}%3%4 + 4A2Ji}}%3%4 }%2 \vtwo{Cauchy's inequality 244Eb @@ -3830,7 +3845,7 @@ \indexheader{cellularity} \vfive{cellularity of a pre- or partially ordered set {\bf 511B}, 511Db, -511H, 511Xf, 513Bc, 513Gc, 513Ya, 514Nc, 514Ud, 528Qb, 528Ye, 537G, 5A4Ad +511H, 511Xh, 513Bc, 513Gc, 513Ya, 514Nc, 514Ud, 528Qb, 528Ye, 537G, 5A4Ad }%5 \vthree{\ifnum\volumeno<5{cellularity }\else{----- }\fi @@ -3841,7 +3856,7 @@ 438Xc, 443Ya\vfive{, {\bf 511Db}, 511I, 514Bb, 514D, 514E, 514Hb, 514J, 514K, 514Nc, 514Xc, 514Xs, 514Yf, 515E, 515F, 521Ob, 521Pa, 523Ya, -{\it 524M}, {\it 524Pb}, {\it 524Tb}, +{\it 524M}, {\it 524Qb}, {\it 524Ub}, 526D, 528Pa, 528Qb, 528Xg, 528Ye, 529Ba, 531Ab, 531F}}; %4%5 }%3 cellularity of Boolean algebra, also $\hc$ @@ -3851,7 +3866,8 @@ 514Bb, 514Hb, 514J, 514Nc, {\bf 5A4Ad}, 5A4B}}; }%3 -\vthree{----- {\it see also} ccc ({\bf 316A}), magnitude ({\bf 332Ga})\vfive{, +\vthree{----- {\it see also} ccc ({\bf 316A}), +magnitude ({\bf 332Ga})\vfive{, saturation ({\bf 511B}), {\bf 511Db}, {\bf 5A4Ad})}%5 }%3 @@ -3876,7 +3892,7 @@ 514B-514E, %514Bd 514Ca 514D 514E 514Hb, 514Ja, 514Nd, 514Xc, 514Xe, 516Lc, 521Jc, 524Me, 524Yc, 528Pb, 528Qc, 528Xg, 528Ye, 539H; - (of a pre- or partially ordered set) {\bf 511Bg}, 511De, 511H, 511Xf, + (of a pre- or partially ordered set) {\bf 511Bg}, 511De, 511H, 511Xh, 511Ya, 513Ee, 513Gd, 514A, 514Nd, 516Kc, 528Qc, 528Ye }%5 @@ -3904,10 +3920,10 @@ \indexheader{chain} \vthree{chain condition (in Boolean algebras or topological spaces\vfive{ or pre-ordered sets}) {\it see}\vfive{ cellularity -({\bf 511B}, {\bf 511D}, {\bf 5A4A}), +({\bf 511B}, {\bf 511D}, {\bf 5A4Ad}), centering number ({\bf 511B}, {\bf 511D}), linking number ({\bf 511B}, {\bf 511D}), saturation ({\bf 511B}, {\bf 511D}, -{\bf 5A4A}),} ccc ({\bf 316A})\vfive{, +{\bf 5A4Ad}),} ccc ({\bf 316A})\vfive{, $\sigma$-linked ({\bf 511De}), $\sigma$-$m$-linked ({\bf 511De})} }%3 @@ -3925,7 +3941,8 @@ }%5 CTP \indexiiheader{change} -\vtwo{change of variable in integration \S235, 263A, 263D, 263F, 263G, 263I, 263Xc, 263Xe, 263Yc +\vtwo{change of variable in integration \S235, +263A, 263D, 263F, 263G, 263I, 263J, 263Xc, 263Xe, 263Yc }%2 \indexivheader{character} @@ -3973,7 +3990,7 @@ {\it chap.\ 56}, {\it 5A3Ce}}}}}; %2%3%4%5 {\it see also} countable choice -\vtwo{choice function {\bf 2A1J}\vfive{, 561A, {\it 561D}}%5 +\vtwo{choice function {\bf 2A1J}\vfive{, 561A, 561D, 561Ye}%5 }%2 \indexivheader{Choquet} @@ -4065,14 +4082,14 @@ \vfour{closed subgroup of a topological group 443P-443U, %443P 443Q 443R 443S 443T 443U -443Xr, 443Xt, 443Xx, 443Ym, {\it 449Yk}, 493Xe, 4A5Jb, 4A5Mc; +443Xr, 443Xt, 443Xx, 443Yq, 493Xf, 4A5Jb, 4A5Mc; {\it see also} compact subgroup }%4 \indexheader{closure} \vtwo{closure of a set {\bf 2A2A}, 2A2B, {\bf 2A3D}, 2A3Kb, 2A5E\vthree{, 3A5Bb\vfour{, - {\it 475Ca}, {\it 475R}, 4A2Bg, 4A2Rd, 4A2Sa, 4A4Bg}}; %3%4 + {\it 475Ca}, {\it 475R}, 4A2Bg, 4A2Rd, 4A2Sa, 4A4Bg, 4A5Em}}; %3%4 {\it see also} essential closure ({\bf 266B}\vfour{, {\bf 475B}}) }%2 @@ -4081,7 +4098,7 @@ }%4 \indexheader{cluster} -\vtwo{cluster point\vthree{ (of a filter) {\bf 3A3L}\vfive{, 561Xi}; } +\vtwo{cluster point\vthree{ (of a filter) {\bf 3A3L}\vfive{, 561Xj}; } (of a sequence) {\bf 2A3O}\vfour{, 4A2Fa, 4A2Gf\vfive{, 5A4Ce}}%4%5 }%2 @@ -4104,43 +4121,43 @@ %Cob%Coc%Cod \indexvheader{codable} -\vfive{codable Baire function {\bf 562Rc} +\vfive{codable Baire function {\bf 562Tc} }%5 %for spelling see Fowler, "mute e" -\vfive{codable Baire set {\bf 562R}, 562Xk, 562Xl, 564Ec +\vfive{codable Baire set {\bf 562T}, 562Xk, 562Xl, 564Ec }%5 -\vfive{----- algebra of codable Baire sets 562R, 562S +\vfive{----- algebra of codable Baire sets 562T, 562U }%5 -\vfive{codable Borel equivalence {\bf 562N}, 562S +\vfive{codable Borel equivalence {\bf 562P}, 562U }%5 -\vfive{codable Borel function {\bf 562J}, 562K, 562L, 562Xd, 562Xf, -562Xi, 563Xa, 564Ea, 564M, 567Eb +\vfive{codable Borel function {\bf 562L}, 562M, 562N, 562Xd, 562Xf, +562Xi, 562Ya, 563Xa, 564Ea, 564M, 567Eb }%5 -\vfive{codable Borel set {\bf 562Ag}, 562C, 562E, 562I, 562Lf, 562Xb, -562Xk, 562Xl, 567Eb +\vfive{codable Borel set {\bf 562Bd}, 562D, 562F, 562K, 562Nf, 562Xb, +562Xk, 562Xl, 562Ya, 562Yb, 567Eb }%5 -\vfive{----- algebra of codable Borel sets 562Ca, 562D, 562S, 565Ea +\vfive{----- algebra of codable Borel sets 562Da, 562E, 562U, 565Ea }%5 \indexvheader{codable family} -\vfive{codable family of Baire sets 562Ra, 562S, 562Xk, 562Xl, 563Kb +\vfive{codable family of Baire sets 562Ta, 562U, 562Xk, 562Xl, 563Kb }%5 -\vfive{----- of Baire functions {\bf 562Rc}, 564Ad, +\vfive{----- of Baire functions {\bf 562Tc}, 564Ad, 564B-564D, %564B 564C 564D 564F }%5 -\vfive{----- of Borel functions {\bf 562Q}, 562Xj +\vfive{----- of Borel functions {\bf 562S}, 562Xj }%5 -\vfive{----- of Borel sets {\bf 562H}, 562I, 562S, 562Xc, 562Xe, 562Xk, +\vfive{----- of Borel sets {\bf 562J}, 562K, 562U, 562Xc, 562Xe, 562Xk, 562Xl, 563Ba }%5 @@ -4161,7 +4178,7 @@ \vthree{cofinal set (in a\vfive{ pre- or} partially ordered set) {\bf 3A1F}\vfour{\vfive{, - {\bf 511Ba}, 511Xk, 513A, 513E-513G, %513E 513F 513G + {\bf 511Ba}, 511Xm, 513A, 513E-513G, %513E 513F 513G 513If, 513Xa, 514Mb, 514Ne, 514U, 516Ga, 517Da}; %5 {\it see also} closed cofinal set}%4 }%3 cofinal set in poset @@ -4170,7 +4187,7 @@ \vthree{cofinality of a\vfive{ pre- or} partially ordered set {\bf 3A1F}\vfour{, 424Yc\vfive{, - {\bf 511Ba}, 511H, 511Xh, 512Ea, 513Ca, 513E, 513Gb, + {\bf 511Ba}, 511H, 511Xj, 512Ea, 513Ca, 513E, 513Gb, 513I, 513J, 513Xf, 514Nb, 514Uc, {\it 514Xj}, 516Kb, 516Xb, 517E, 528Qa, 528Ye, 529Xb, 542Da, 542H, 542J, 5A1Ad, 5A2A-5A2D %5A2Ab 5A2Bc 5A2C 5A2Db @@ -4178,29 +4195,29 @@ }%3 \vfour{----- of a cardinal 4A1Ac\vfive{, -511Xh, {\it 512Gd}, 513C, 513Ih, 513Xb, 522U, 522Yh, 523Mb, {\it 523O}, -525Ec, {\it 525F}, {\it 525Jb}, 525N-525P, %525N {\it 525O} {\it 525P} +511Xj, {\it 512Gd}, 513C, 513Ih, 513Xb, 522U, 522Yh, 523Mb, {\it 523O}, +525Dc, {\it 525E}, {\it 525Ib}, 525M-525O, %525M {\it 525N} {\it 525O} {\it 532L}, 561Ya, 5A1Ac, 5A1Ed, 5A1H-5A1J, %5A1Ha 5A1Ia 5A1J 5A6A, 5A6C}%5 }%4 -\vfive{----- of an ideal 511F, 522B, 522E, 522H, 522J, 522P, 522U, 522V, +\vfive{----- of an ideal 511Fa, 522B, 522E, 522H, 522J, 522P, 522U, 522V, 522Xa, 523Ye, 534Zb, 526Ga, 526Xc, 526Xg, 527Bb, 529Xe, 539Ib }%5 -\vfive{----- of a null ideal 511Xc, 511Xe, 511Yc, +\vfive{----- of a null ideal 511Xd, 511Xf, 511Yc, 521D-521F, %521Da, 521E, 521Fb, -521H, 521I, 521Ya, 522V, +521H, 521I, 521Xl, 521Ya, 522V, 523B, 523N-523P, %523N {\it 523O} 523P 523Xd, 523Ye, 524I, 524Ja, -524P-524T, %524Pf, 524Q, 524R, 524Sa 524Te +524Q-524U, %524Qf, 524R, 524S, 524Ta 524Ue 524Xj, 537Ba, 537Xa, 544Nd, 552I }%5 % cofinality of a null ideal \vfive{----- of the Lebesgue null ideal 521I, 522B, 522E, 522F, 522P, 522S-522V, %{\it 522S} 522Td 522U 522Va -522Ya, 523N, 524Mc, 524Pf, 524T, +522Ya, 523N, 524Mc, 524Qf, 524U, 526Ga, 526Ye, 528Qc, 528Ye, 529Xb, 529Xe, 531Q, 532Za, 534B, 537Xa 539D, 552I }%5 @@ -4209,8 +4226,8 @@ }%5 \vfive{----- of $[I]^{\le\omega}$ 522Td, 523G, 523Ia, 523Ma, -523N, 523Xd, 523Z, 524Mc, 524Pb, -524R, 524T, 529Xb, 532L, 532Qa, 537Ba, 537S, 539D, 539Xc, +523N, 523Xd, 523Z, 524Mc, 524Qb, +524S, 524U, 529Xb, 532L, 532Qa, 537Ba, 537S, 539D, 539Xc, 546O, 555Yb, 5A1Ee, 5A3Nd }%5 @@ -4237,15 +4254,17 @@ \vfive{\indexheader{coinitiality}} \vfive{coinitiality of a pre- or partially ordered set {\bf 511Bc}, 511Dc, 511H, -512Ea, 521Xl, 524Pb, 524Tb, 538Yn, 547Xd, 5A4Ab, {\it 5A6Ia} +512Ea, 538Yn, 5A4Ab, {\it 5A6Ia}; +{\it see also} $\pi$-weight of a Boolean algebra ({\bf 511Dc}), +$\pi$-weight of a measure ({\bf 511Gb}) }%5 %Coj%Cok%Col%Com \vthree{\indexheader{comeager}} \vthree{comeager set {\bf 3A3Fb}, 3A3G\vfour{, - 494Ed}\vfive{, - 546N}%5 + {\it 494Ed}\vfive{, + 546N}} %4%5 }%3 \indexheader{commutative} @@ -4286,16 +4305,16 @@ \vthree{compact Hausdorff space 364U, 364V, 364Yk, 364Ym, 364Yn, 3A3D, 3A3Ha, {\it 3A3K}\vfour{, 422Gc, {\it 434B}, 437Md, 437Rf, 437T, 437Va, -{\it 452N}, {\it 462Z}, 463Zc, +{\it 452N}, {\it 462Z}, {\it 463Zc}, {\it 481Xh}, 496F, 496Xc, 4A2Fh, 4A2G, 4A2Nh, 4A2Ri, 4A2T, 4A2Ud, 4A3Xd\vfive{, - 511Xl, {\it 515Xc}, 561Xf, 5A4C, 5A4Ec}%5 + 511Xb, {\it 515Xc}, 561Xg, 5A4C, 5A4Ec}%5 }%4 }%3 compact Hausdorff space \vthree{compact linear operator 371Xb, 371Yb, 376Xi, {\bf 3A5La}\vfour{, 444V, 444Xu, 4A4L, 4A4M\vfive{, - 561Xo, 566Yb}}; %4%5 + 561Xr, 566Yb}}; %4%5 {\it see also} weakly compact operator ({\bf 3A5Lb}) }%3 @@ -4315,10 +4334,10 @@ \vfour{compact metrizable space 423Dc, 424Xf, 441Gb, 441Xm, 441Xp, 441Yj, -449Xq, 461M, 461P, {\it 461Xf}, 461Xi, {\it 462J}, +449Xr, 461M, 461P, {\it 461Xf}, 461Xi, {\it 462J}, 463C, {\it 465Xo}, 466Xf, 4A2Tg, 476C, 476Ya, {\it 481P}, 4A2Nh, 4A2P, 4A2Q, 4A2Ud\vfive{, - 526He, 561Yc, 566Xa, 5A4I, 5A4Jc}%5 + 526He, 561Yc, 566Xa, 5A4H, 5A4Ic}%5 }%4 \vfour{compact-open topology {\bf 441Yh}, 441Yi\vfive{, @@ -4331,7 +4350,7 @@ $\pmb{>}${\bf 2A3N}, 2A3R\vthree{, 3A3D\vfour{, {\it 421M}, 421Xn, {\it 461I}, {\it 461J}, 461Xe, 461Xj, {\it \S463}, -4A2Fh, 4A2G, 4A2Jd, 4A2Rg, 4A2Sa, +4A2Fh, 4A2G, 4A2Je, 4A2Rg, 4A2Sa, 4A3Xc, {\it 4A4Bf}, {\it 4A4H}, 4A4Ka, 4A5E\vfive{, 561D}}}; %4%3%5 \vfour{(spaces of compact subsets) 476A; }%4 @@ -4339,13 +4358,13 @@ relatively weakly compact ({\bf 2A5Id}), weakly compact ({\bf 2A5Ic}) }%2 compact set -\vfour{compact subgroup of a topological group 443S, 443Xv, 443Yp +\vfour{compact subgroup of a topological group 443S, 443Xv, 443Yr }%4 \vtwo{compact support, function with 242Xh, 256Be, {\it 256D}, 262Yd-262Yg\vfour{, %262Yd 262Ye 262Yf 262Yg 443P, 444Xs, {\it 473Bf}, {\it 473Db}, {\it 473Ed}, -473H, {\it 475K}, {\it 475Nb}, {\it 479T}, {\it 479U}, +473H, {\it 475K}, {\it 475Nc}, {\it 479T}, {\it 479U}, {\bf 4A2A}, 4A2Ge}; %4 {\it see also} $C_k(X)$, $C_k(X;\Bbb C)$ }%2 @@ -4355,14 +4374,15 @@ \vfour{compact topological group 441Xd, 441Xk, 441Yq, {\it 443Ag}, 443U, 444Xf, 445A, 445Xi, 445Xm, -446B, 446C, 446Yb, {\it 447Ya}, 452T, 491H, 491Xm, 491Yi, 494Xb, 494Yj, +446B, 446C, 446Yb, {\it 447Ya}, +452T, 491H, 491Xm, 491Yi, 494Xb, 494Yj, 4A5Ja, 4A5T\vfive{, 566Yb} %5 }%4 \vtwo{compact topological space {\bf $\pmb{>}$2A3N}\vthree{, 3A3Dd, 3A3J\vfour{, - {\it 415Yb}, 462Yd, 4A2G, 4A2Jf, 4A2Kb, 4A2Lf, 4A2Tb, 4A3O}; %4 + {\it 415Yb}, 462Yd, 4A2G, 4A2Jg, 4A2Kb, 4A2Lf, 4A2Tb, 4A3O}; %4 {\it see also} compact Hausdorff space\vfour{, countably compact ({\bf 4A2A}), Eberlein compactum {\bf 467O}}, locally compact ({\bf 3A3Ah})\vfour{, @@ -4428,7 +4448,7 @@ }%2 \vtwo{complete locally determined measure (space) 213C, 213D, 213H, 213J, -213L, 213O, 213Xg, 213Xi, 213Xl, 213Yd, 213Ye, 214I, +213O, 213Xg, 213Xk, 213Xl, 213Ye, 213Yf, 214I, 216D, 216E, 234Nb, 251Yc, 252B, 252D, 252N, 252Xc, 252Ye, 252Ym, 252Yq-252Ys, %252Yq, 252Yr, 252Ys, 252Yv, 253Yj, 253Yk\vthree{, @@ -4456,7 +4476,7 @@ 214I, {\it 214K}, {\it 216A}, {\it 216C-216E}, %{\it 216C 216D 216E} {\it 216Ya}, 234Ha, {\it 234I}, 234Ld, 234Ye, -235Xl, {\it 254Fd}, 254G, {\it 254J}, +235Xl, {\it 254Fd}, 254G, {\it 254J}, 256Ad, 257Yb, {\it 264Dc}\vthree{, 321K, 341J, 341K, 341M, 341Nb, {\it 341Xd}, 341Yd, {\it 343B}, {\it 343Xf}, {\it 344C}, {\it 344I}, {\it 344K}, @@ -4472,7 +4492,7 @@ \vtwo{complete metric space {\it 224Ye}\vthree{, 323Mc, {\it 323Yd}, {\it 377Xf}, 383Xj, 3A4Fe\vfour{, 434Jg, 437Rg, 437Yy, 438H, 438Xh, 479Yf, 4A2M, 4A4Bj\vfive{, - 524C, 556Xb, 561Ea, 561Yc, 561Ye, 564O, 566Xa, 5A4I}}}; %5%4%3 + 524C, 556Xb, 561Ea, 561Yc, 561Ye, 564O, 566Xa, 5A4H}}}; %5%4%3 {\it see also} Banach space ({\bf 2A4D})\vfour{, Polish space ({\bf 4A2A})} }%2 complete metric space @@ -4487,13 +4507,13 @@ }%4 \vthree{complete uniform space 323Gc, {\bf 3A4F}, 3A4G, 3A4H\vfour{, - 4A2Jd, 4A5Mb}; + 4A2Je, 4A5Mb}; {\it see also} completion ({\bf 3A4H}) }%3 \vfour{complete (in `$\kappa$-complete filter') 351Ye, 368F, 438Yb, {\bf 4A1Ib}, 4A1J, 4A1K\vfive{; - (in `$\kappa$-complete ideal') {\it see under} additive ({\bf 511F})}%5 + (in `$\kappa$-complete ideal') {\it see under} additive ({\bf 511Fa})}%5 }%4 \vthree{complete {\it see also} Dedekind complete ({\bf 314Aa}), @@ -4516,7 +4536,7 @@ 327Ya, 332Xo, 362Ad, 362B, 362D, 362Xe-362Xg, %{\it 362Xe}, {\it 362Xf}, 362Xg, 363K, {\it 363S,} 365Ea, 391Xg, 395Xe\vfour{, - 438Xc, 457Xh, 461Xn\vfive{, + 438Xc, 457Xg, 461Xn\vfive{, {\it 538Rb}, 538Sb}}; %4%5 {\it see also} $M_{\tau}$ }%3 completely additive functional on B alg @@ -4545,7 +4565,7 @@ 416T, 416Xj, 416Xl, 416Xw, {\it 434Jg}, {\it 434Yd}, {\it 434Ye}, {\it 436Xl}, {\it 437Kc}, {\it 437L}, {\it 453Cb}, 4A2F, 4A2Hb, 4A2J\vfive{, - {\it 561G}, 561Xj, 561Yj, + {\it 561G}, 561Xm, 561Ye, {\it 566Af}, 566Xj, 566Yb, 564I, 564Ya, 5A4Ed}}%4%5 }%3 completely regular topological space @@ -4561,7 +4581,7 @@ }%5 \vtwo{\ifnum\volumeno<3{completion }\else{----- }\fi (of a measure (space)) -\S212 ({\bf 212C}), 213Fa, 213Xa, 213Xb, 213Xk, 214Ib, 214Xi, 216Yd, +\S212 ({\bf 212C}), 213Fa, 213Xa, 213Xb, 213Xi, 214Ib, 214Xi, 216Yd, {\it 232Xe}, 234Ba, 234Ke, {\it 234Lb}, 234Xc, 234Xl, 234Ye, 234Yo, {\it 235D}, 241Xb, 242Xb, 243Xa, 244Xa, 245Xb, 251T, 251Wn, 251Xr, 252Ya, 254I, {\it 256C}\vthree{, @@ -4569,7 +4589,7 @@ 411Xc, 411Xd, 412H, 412Xi, 412Xj, 413E, {\it 416Xn}, 433Cb, 451G, 451Yn, 452A-452C, %452A 452B 452C 452Xg, {\it 452Xt}, 465Ci, 491Xr\vfive{, - 511Xd, {\it 551Xb}, {\bf 563Ab}, 563I}}}%5%4%3 + 511Xe, {\it 551Xb}, {\bf 563Ab}, 563I}}}%5%4%3 }%2 completion of measure \vthree{----- (of a metric space) {\it 392H}, 3A4Hc @@ -4584,7 +4604,7 @@ \vfour{----- (of a submeasure) {\bf 496Bc}, 496K, 496Xd }%4 -\vfour{----- (of a topological group) 443K, 445Ya, 449Xh, 493Xa, 4A5N +\vfour{----- (of a topological group) 443K, 445Ya, 449Xi, 493Xa, 4A5N }%4 completion \vthree{----- (of a uniform space) 323Xh, {\it 325Ea}, 325Yc, {\bf 3A4H} @@ -4594,7 +4614,7 @@ 415Xk, 416U, 417Xu, 417Xv, {\it 419D}, 419E, 434A, 434Q, 434Xa, 434Xr, {\it 434Ya}, {\it 435A}, 439J, 443M, 451U, 454T, 455K, 467Xj, 491Md\vfive{, - 532D, 532E, 532H, 532Xf, {\it 533Xg}}; %5 + 532A, 532D, 532E, 532H, 532Xf, {\it 533Xg}}; %5 {\it see also} inner regular with respect to zero sets\vfive{, $\Mahcr$ ({\bf 532A})}%5 }%4 completion regular measure @@ -4636,6 +4656,9 @@ %Con +\indexvheader{concatenation} +concatenation (of finite sequences) {\bf 562Aa} + \indexiiiheader{concave} \vthree{concave function {\bf 385A} }%3 @@ -4648,7 +4671,7 @@ \vfour{concentration of measure 476F-476H, %476F 476G 476H 476K, 476L, 476Xc, 476Xe, 492D, 492E, 492H, 492I, 492Xb-492Xd, %492Xb, 492Xc, 492Xd, -493F +{\it 493C} }%4 \vfour{concentration by partial reflection 476D, 476E, 476Xb @@ -4672,7 +4695,7 @@ 233Ye, 235Yb, 242J, 246Ea, 253H, 253Le, 275Ba, 275H, 275I, 275K, 275Ne, 275Xj, 275Yb, 275Yo, {\it 275Yp}\vthree{, 365R, 365U, 367Q, 367Yt, {\it 369Xq}, 372J\vfour{, - 452Qb, 452Xr, 455Cb, 455Ec, 455O, 455S, + 452Qb, 452Xr, 455Cb, 455Ec, 455O, {\it 458A}, 458F, 458Xf, 465M, 465Xt, 478Vb, 494Ad, 494N\vfive{, 538Kb, 538Xs, 538Yg}}}%3%4%5 }%2 conditional expectation @@ -4770,9 +4793,10 @@ {\bf 2A2C}, 2A2G, {\bf 2A3B}, 2A3H, 2A3Nb, 2A3Qb\vthree{, 3A3C, {\it 3A3Eb}, 3A3Ib, 3A3Nb, 3A3Pb\vfour{, {\it 418D}, {\it 418L}, 422Dc, 434Xe, 434Xi, {\it 473Db}, 4A2B, 4A2C, -4A2Eb, 4A2F, 4A2G, 4A2Ia, 4A2Kd, {\it 4A2Ld}, 4A2Ro, 4A2Sb, +4A2E-4A2G, %4A2Eb, 4A2F, 4A2G, +4A2Ia, 4A2Kd, {\it 4A2Ld}, 4A2Ro, 4A2Sb, 4A3Cd, 4A3Kc, 4A3L, 4A5Fa\vfive{, - 562Kd, 562Rb}}}}%4%5%3%2 + 562Md, 562Tb}}}}%4%5%3%2 \vthree{continuous at a point {\bf 3A3C} }%3 @@ -4788,7 +4812,7 @@ \vtwo{continuous linear operator 2A4Fc\vthree{, 375E\vfour{, - {\it 456B}, {\it 456Ib}, {\it 456K}, 461B, {\it 466Xo}, {\it 466Xq}, + {\it 456B}, {\it 456Ib}, {\it 456K}, 461B, {\it 466Xm}, {\it 466Xp}, 4A4B, {\it 4A4Gc}\vfive{, 537Hb, 567Hc}}}; %3%4%5 {\it see also} bounded linear operator ({\bf 2A4F}) @@ -4798,12 +4822,16 @@ continuous ({\bf 232Aa}) }%2 +\vtwo{continuous on the right {\bf 224Xm} +}%2 + \vthree{continuous outer measure {\it see} Maharam submeasure ({\bf 393A}) }%3 \allowmorestretch{468}{ \vtwo{continuous {\it see also }\vfour{almost continuous ({\bf 411M}),} -\vthree{order-continuous ({\bf 313H}),} semi-{\vthsp}continuous ({\bf 225H}\vfour{, +\vthree{order-continuous ({\bf 313H}),} +semi-{\vthsp}continuous ({\bf 225H}\vfour{, {\bf 4A2A}})\vthree{, uniformly continuous ({\bf 3A4C})} }%2 }% end of allowmorestretch @@ -4814,7 +4842,7 @@ \vfour{continuum hypothesis 425E, 444Yf, {\it 463Yd}, 463Ye, {\bf 4A1Ad}\vfive{, - {\it 515Ya}, 517Od, 518Xg, 532P, 535G, 535I, 536Cd, 552Xc, 552Xd, + {\it 515Ya}, 517Od, 518Xg, 532P, 535G, 535I, 536Dd, 552Xc, 552Xd, 554I, 556 {\it notes}}; %5 {\it see also} generalized continuum hypothesis\vfive{ ({\bf 5A6Aa})}%5 }%4 @@ -4833,23 +4861,24 @@ \vtwo{convergence in mean (in $\eusm L^1(\mu)$ or $L^1(\mu)$) {\bf 245Ib} }%2 +\indexiiheader{convergence in measure} \vtwo{convergence in measure (in $L^0(\mu)$) \S245 ($\pmb{>}${\bf 245A}), 246J, 246Yc, 247Ya, 253Xe, 255Yh, 285Yr\vfour{, 416Xk, 418R, 418S, 418Yj, 444F, 445I, 448Q, 448R, 465Xk, 465Xs, 493E}%4 }%2 cgence in measure -\vtwo{----- (in $\eusm L^0(\mu)$) \S245 ($\pmb{>}${\bf 245A}), +\vtwo{----- ----- (in $\eusm L^0(\mu)$) \S245 ($\pmb{>}${\bf 245A}), 271Yd, 272Yd, 274Yf, 285Xs\vfour{, \S463, {\it 464E}, 464Yb, 465G, 465Xl\vfive{, \S536}}%4%5 }%2 -\vtwo{----- (in the algebra of measurable sets) {\bf 232Ya}\vfour{, +\vtwo{----- ----- (in the algebra of measurable sets) {\bf 232Ya}\vfour{, 474T}%4 }%2 -\vthree{----- (in $L^0(\frak A,\bar\mu)$) {\bf 367L}, +\vthree{----- ----- (in $L^0(\frak A,\bar\mu)$) {\bf 367L}, 367M-367W, %367M 367N 367O 367P 367R 367S 367T 367U 367V 367W 367Xo, 367Xp, 367Xr, 367Xt, 367Xv-367Xx, %367Xv 367Xw 367Xx 367Xz, 367Yp, 367Ys, 369M, 369Xf, 369Ye, 372Yd, 375E, @@ -4858,7 +4887,7 @@ 529Bb}}%4%5 }%3 convergence in measure in L^0(\frak A,\bar\mu) -\vtwo{----- (of sequences) 245Ad, 245C, +\vtwo{----- ----- (of sequences) 245Ad, 245C, 245H-245L, %245H 245I 245J 245K 245L 245Xd, 245Xf, 245Xl, 245Yh, 246J, 246Xh, 246Xi, 271L, 273Ba, 275Xl, 276Yf\vthree{, @@ -4887,7 +4916,7 @@ sequence {\bf 135D}\vtwo{, 245Yi, {\bf 2A3M}, 2A3Sg\vthree{, 3A3Lc, 3A3Pa\vfour{, 4A2Gh, 4A2Ib, 4A2Le, 4A2Rf\vfive{, - 536Ca, 5A4Ce}}}; %3%4%5 + 536Da, 5A4Ce}}}; %3%4%5 {\it see also} convergence in measure ({\bf 245Ad})\vthree{, order*-convergent ({\bf 367A})}\vfour{, pointwise convergence, statistically convergent ({\bf 491Xx})} @@ -4903,7 +4932,7 @@ 242K, 242Yi, 242Yj, 242Yk, {\it 244Xm}, {\it 244Yh}, 244Ym, {\it 255Yj}, {\it 275Yh}\vthree{, {\it 365Rb}, {\bf 367Xx}, 369Xb, 369Xc, 369Xd, 373Xb\vfour{, - {\bf 461A}, 461C, 461D, 461K, 461Xa, 475Yf, 476Yb}}; + {\bf 461A}, 461C, 461D, 461K, 461Xa, 475Ye, 476Yb}}; {\it see also} mid-convex ({\bf 233Ya}) }%2 convex function @@ -4923,8 +4952,7 @@ {\bf 2A5E}\vthree{, {\it 326H}, 326Yk, {\it 351Ce}, 3A5C, 3A5Ee, 3A5Md\vfour{, 461Ac, {\it 461D}, {\it 465Xb}, 475R-475T, %475R 475S 475T -475Xa, 475Xk, 479Xn, {\it 484Xc}, 4A4Db, 4A4E, {\it 4A4F}, -{\it 4A4Ga}; +475Xa, 475Xk, 479Xn, {\it 484Xc}, 4A4Db, 4A4E, {\it 4A4Ga}; {\it see also} order-convex ({\bf 4A2A})}}%3%4 }%2 convex set @@ -4932,11 +4960,11 @@ \vfour{----- compact set 437T, 438Xo, 461E, 461J-461P, %461J 461K 461L 461M 461N 461O 461P -461Xh, 461Xi, 461Xk, 461Xq, 461Yb, 461Yc, {\it 463G}, 463Xd, +461Xh, 461Xi, 461Xk, 461Xq, 461Yb, 461Yc, 463G, 463Xd, 4A4E-4A4G %4A4Ef 4A4F 4A4G }%4 -\vthree{----- {\it see also} cone ({\bf 3A5B})\vfour{, {\bf 4A2A}}) +\vthree{----- {\it see also} cone ({\bf 3A5B}) }%3 % convex @@ -4952,7 +4980,8 @@ 255F-255K, %255F, 255G, 255H, 255I, 255J, 255K, {\bf 255O}, 255Xa-255Xg, %255Xa 255Xb 255Xc 255Xd 255Xe 255Xf 255Xg 255Ya, 255Yc, 255Yd, 255Yf, 255Yg, 255Yk, 255Yl, {\bf 255Yn}, -262Xj, 262Yd, 262Ye, 262Yh, 263Ya, 282Q, 282Xt, 283M, 283Wd, 283Wf, 283Wj, 283Xl, 284J, 284K, 284O, 284Wf, 284Wi, 284Xb, 284Xd\vthree{, +262Xj, 262Yd, 262Ye, 262Yh, 263Ya, 282Q, 282Xt, 283M, 283Xl, +283Wg, 283Wh, 283Wj, 284J, 284K, 284O, 284Wf, 284Wi, 284Xb, 284Xe\vthree{, 373Xg, 376Xa, 376Xd\vfour{, {\bf 444O}, 444P-444S, %444P 444Q 444R 444S 444Xr-444Xt, %444Xr 444Xs 444Xt @@ -4970,12 +4999,12 @@ {\bf 444A}, 444B-444E, %444B 444C 444D 444E 444Qa, 444Sc, 444Xa-444Xc, %444Xa, 444Xb, 444Xc, 444Xe, 444Xf, 444Xq, 444Xw, 444Yb, 444Yj, 444Yq, 445D, 455P, 455R, -455T, 455Xe, 455Xk, -455Yd, 458Yc, 466Xr, 479Xc, 495Ab}%4 +455U, 455Xe, 455Xk, +455Yc, 455Yd, 458Yc, 466Xo, 479Xc, 495Ab}%4 }%3 }%2 convolution of measures -\vtwo{convolution of measures and functions {\it 257Xe}, 284Xo, 284Yi\vfour{, +\vtwo{convolution of measures and functions {\it 257Xe}, 284Xp, 284Yi\vfour{, {\bf 444H}, 444I, {\bf 444J}, 444K, 444M, 444P, 444T, 444Xh-444Xk, %444Xh 444Xi 444Xj 444Xk 444Xq, 444Yj, 449J, 449Yc, 479H, 479Ib, 479Xc}%4 @@ -5009,7 +5038,7 @@ }%3 countable choice, axiom of {\it 134C}\vtwo{, 211P\vfive{, - 562Cb, \S566, 567Cb, 567H, 567K, 567Xh, 567Yc}}%2%5 + 562Db, \S566, 567Cb, 567H, 567K, 567Xh, 567Yc}}%2%5 \vfive{----- ($AC(\Bbb R;\omega)$) 567D-567F, %567D 567E 567F 567I, 567Xb, 567Xd, 567Yf @@ -5038,7 +5067,7 @@ 451N, 451O, 453Fa, 453I, 453J, 491Eb, 491Yn, 491Yo, 4A2N-4A2Q, %4A2N 4A2O 4A2Pa 4A2Qh 4A3E, 4A3F, 4A3Rc, 4A3Xa, 4A3Xg, 4A3Yb\vfive{, - 522Va, 529Yb, 532E, 561Xe, 561Ye}%5 + 522Va, 529Yb, 532E, 561Xf, 561Yd}%5 }%4 countable network \vfour{countable separation property {\it see} @@ -5072,7 +5101,7 @@ 327B, 327C, 327F, 327Xc-327Xe, %327Xc, 327Xd, 327Xe, 362Ac, 362B, 363S, 363Yg, 391Xg, 393Xe, {\it 393Yg}\vfour{, - 438Xc, 457Xh, 461Xn\vfive{, + 438Xc, 457Xg, 461Xn\vfive{, 538Yp, 545F, 566F, 567J}}; %4%5 {\it see also} completely additive ({\bf 326N}), countably subadditive ({\bf 393Bb}), $M_{\sigma}$ @@ -5107,7 +5136,7 @@ \vfour{countably compact set, topological space 413Ye, 421Ya, 422Yc, 434M, 434N, 435Xo, 436Yc, 462B, 462C, 462F, 462G, 462I, 462J, -462Xb, 462Ya, 463L, {\bf $\pmb{>}$4A2A}, 4A2Gf, 4A2Lf\vfive{, +462Xb, 462Ya, 463L, 463M, {\bf $\pmb{>}$4A2A}, 4A2Gf, 4A2Lf\vfive{, 564Xb, 566Xa, 566Yb}; %5 {\it see also} relatively countably compact ({\bf 4A2A}) }%4 countably compact @@ -5178,10 +5207,10 @@ %Cov \vfour{\indexheader{covariance}} \vfour{covariance matrix (of a Gaussian distribution) {\bf 456Ac}, 456B, -456C, 456J, 456Q, 456Xc, 477D, 477Xd, 477Yb, 494F +456C, 456J, 456Q, 456Xc, 477D, 477Xd, 477Yb, 494Fb }%4 -\vfour{----- (of a Gaussian measure) {\bf 466Xo} +\vfour{----- (of a Gaussian measure) {\bf 466Xm} }%4 \vfour{\indexheader{covariant} @@ -5197,26 +5226,26 @@ Jensen's Covering Lemma}}%4 }%2 -\vfive{covering number of an ideal {\bf 511Fc}, 511J, 512E, 513Cb, +\vfive{covering number of an ideal {\bf 511Fd}, 511J, 512E, 513Cb, 523Ye-523Yg, %523Ye 523Yf 523Yg 526Xc, 527Bb, 529Xg, 539Gb, 541O }%5 -\vfive{----- ----- (of a null ideal) 511Xc-511Xe, %511Xc 511Xd 511Xe +\vfive{----- ----- (of a null ideal) 511Xd-511Xf, %511Xd 511Xe 511Xf 521D-521H, %521Db 521E 521Fa 521G 521Ha 521Jb, 521Xc, 521Xd, 521Xe, 522Va, {\it 522Xe}, 523B, 523Db, 523F, 523G, 523P, 523Xd, 523Ye, 523Yg, -524Jb, 524Md, 524Na, 524Pc, 524Sb, 524Tc, -524Xf, 524Yc, 525H, 525K, 525Xb, 529Xg, +524Jb, 524Md, 524Na, 524Qc, 524Tb, 524Uc, +524Xf, 524Yc, 525G, 525J, 525Xb, 529Xg, 531Xh, 533E, 533H, 533J, 533Yb, 533Yc, -534B, 536Cf, 536Xa, 536Xb, 537Ba, +534B, 536Df, 536Xa, 536Xb, 537Ba, 537N-537S, %537N 537O 537P 537Q 537R 537S 537Xh, {\it 538Yd}, 544B, 544M, {\it 544N}, 552G, 552Ob, 552Xb, 552Yb, 555F }%5 \vfive{----- ----- (of the Lebesgue null ideal, $\cov\Cal N$) 521G, 522B, 522E, 522G, -{\it 522S}, 522T, 522Xf, 522Xg, 522Yb, 523F, 525Xc, 529H, 529Xg, +{\it 522S}, 522T, 522Xf, 522Xg, 522Yb, 523F, 525Xb, 525Xc, 529H, 529Xg, 532O, 532P, 534Bd, 534Yc, 536Ya, 537Xg, 538He, 538Yi, 544Zf, 552G, 552Xb }%5 covering of N @@ -5252,7 +5281,7 @@ \indexheader{cozero} \vthree{cozero set {\bf 3A3Qa}\vfour{, 412Xh, {\it 416Xj}, 421Xg, 435Xn, -443N, {\it 443Yl}, {\it 496Ye}, 4A2Cb, 4A2F, 4A2Lc\vfive{, +443N, {\it 443Yn}, {\it 496Ye}, 4A2Cb, 4A2F, 4A2Lc\vfive{, {\it 533Ga}, {\it 533J}}}%4%5 }%3 @@ -5270,14 +5299,15 @@ }%3 \indexheader{cylinder} -\vtwo{cylinder (in `measurable cylinder') {\bf 254Aa}, 254F, {\it 254G}, +\vtwo{cylinder 265Xf; + (in `measurable cylinder') {\bf 254Aa}, 254F, {\it 254G}, {\it 254Q}, 254Xa }%2 \vfour{\indexheader{cylindrical} cylindrical $\sigma$-algebra (in a locally convex space) {\it 461E}, 461Xg, 461Xi, -464R, 466J, {\it 466N}, 466Xc, 466Xd, 466Xf, 466Xo, +464R, 466J, {\it 466N}, 466Xc, 466Xd, 466Xf, 466Xm, 491Yd, {\bf 4A3T}, 4A3U, 4A3V }%4 @@ -5314,8 +5344,8 @@ }%2 \indexheader{decomposition} -\vtwo{decomposition (of a measure space) {\bf 211E}, {\it 211Ye}, 213O, -{\it 213Xh}, 214Ia, 214L, 214N, {\it 214Xh}\vthree{, +\vtwo{decomposition (of a measure space) {\bf 211E}, {\it 211Ye}, 213Ob, +{\it 213Xj}, 214Ia, 214L, 214N, {\it 214Xh}\vthree{, {\it 322M}\vfour{, 412I, 416Xf, 417Xe, 495Xc}} %3%4 }%2 @@ -5357,7 +5387,7 @@ 382Q-382S, %382Q 382R 382S 382Xd-382Xi, %382Xd 382Xe 382Xf 382Xg 382Xh 382Xi 384D, 384J, 393Eb, 393K, 393Xc\vfour{, - 438Xc, {\it 448Ya}, 494Hb, {\it 496Bb}, 496Ya\vfive{, + 438Xc, {\it 448Ya}, 494Hb, 494Xm, {\it 496Bb}, 496Ya\vfive{, 514F, 514G, 514I, 514Sa, 514Xe, 514Yg, 514Yh, 515Cb, 515D, 515F, 515H-515J, %515H 515I 515J 515N, 517Xc, 518D, 518Fc, 518K, 518Qb, 518S, 518Xg, 518Xi, 518Yc, 527Nb, @@ -5399,6 +5429,8 @@ 368Yb, 369Xp }%3 +\wheader{Dedekind}{0}{0}{0}{72pt} + \vthree{Dedekind $\sigma$-complete Boolean algebra 314C-314G, %314C, 314D, 314Eb, 314Fb 314Gb, 314Jb, 314M, 314N, 314Xa, 314Xg, 314Ye, 314Yf, {\it 315P}, {\it 316C}, @@ -5414,14 +5446,15 @@ 382S, 382Xk, 382Xl, 382Ya, 382Yd, 393Bc, 393C, 393Ea, 393F, 393I, 393O, 393Pe, 393S, 393Xb, 393Xe, 393Xj, 393Yc\vfour{, - 424Xd, \S448, 461Qa, {\it 491Xn}, 494Xm, 494Yk, 496Ba\vfive{, + 424Xd, \S448, 461Qa, {\it 491Xn}, 494Yk, 496Ba\vfive{, 515Mb, 518L, 535Xd, 535Xe, 538Yp, 539L-539N, %539L 539M 539N 539Pc, 539Ya, 546Ba, 555Jb, 556Af, 556Xb, 556Yc, -562T, 566F, 566L, 566O, 566Xc, 566Xg, 567J, 567Yf}}%4%5 +562V, 566F, 566L, 566O, 566Xc, 566Xg, 567J, 567Yf}}%4%5 }%3 Ded \sigma-cplete B alg -\vthree{Dedekind $\sigma$-complete partially ordered set {\bf 314Ab}, 315De, 367Bf\vfour{, +\vthree{Dedekind $\sigma$-complete partially ordered set {\bf 314Ab}, +315De, 367Bf\vfour{, 466G}; {\it see also} Dedekind $\sigma$-complete Boolean algebra, Dedekind $\sigma$-complete Riesz space @@ -5432,7 +5465,7 @@ 354Xn, 354Yi, {\it 354Ym}, 356Xc, 356Xd, 363M-363P, %363Ma 363N 363O 363P 364B, 364D\vfive{, - 561Xm}%5 + 561Xp}%5 }%3 }%2 @@ -5455,11 +5488,11 @@ \vtwo{dense set in a topological space 136H, 242Mb, 242Ob, 242Pd, 242Xi, 243Ib, 244H, 244Pb, 244Xk, 244Yj, 254Xo, 281Yc, {\bf 2A3U}, 2A4I\vthree{, - {\it 313Xj}, 314Xk, 323Dc, 367N, {\bf 3A3E}, 3A3G, 3A3Ie, {\it 3A4Ff}\vfour{, - 412N, 412Yc, 417Xt, -4A2Bj, {\it 4A2Ma}, {\it 4A2Ni}, -{\it 4A2Ua}\vfive{, - 514Hd, 514Mb, 516I, 516Xg, 5A4Ac, 5A4H}}; + {\it 313Xj}, 314Xk, 323Dc, 367N, {\bf 3A3E}, 3A3G, 3A3Ie, +{\it 3A4Ff}\vfour{, + 412N, 412Yc, 417Xt, 4A2Bj, {\it 4A2Ma}, {\it 4A2Ni}, +{\it 4A2Ua}, 4A4Eh\vfive{, + 514Hd, 514Mb, 516I, 516Xg, 561Ea, 561Ye, 5A4Ac}}; {\it see also} nowhere dense ({\bf 3A3Fa}), order-dense ({\bf 313J}, {\bf 352Na}), quasi-order-dense ({\bf 352Na}) }%3 @@ -5528,7 +5561,8 @@ derivative of a function\vtwo{ (of one variable) 222C, 222E-222J, %222E 222F 222G 222H 222I 222J 222Yd, 225J, {\it 225L}, {\it 225Of}, {\it 225Xc}, {\it 226Be}, 282R; - (of many variables) {\bf 262F}, 262G, 262P\vfour{, 473B, 473Ya}; }%2%4 + (of many variables) {\bf 262F}, 262G, 262P, 263Ye\vfour{, + 473B, 473Ya}; }%2%4 {\it see\vfour{ also}}\vfour{ gradient,} partial derivative %derivative @@ -5602,9 +5636,10 @@ 225Of}, {\it 225Xc}, {\it 225Xn}, 233Xc, 252Ye, 255Xd, 255Xe, 262Xk, 265Xd, {\it 274E}, 282L, 282Rb, 282Xs, 283I-283K, %283I, 283J, 283K, -{\it 283Xm}, 284Xc, 284Xk\vfour{, +{\it 283Xm}, 284Xc, 284Xl\vfour{, {\it 477K}, 483Xh}; %4 - (of many variables) {\bf 262Fa}, 262Gb, 262I, 262Xg, 262Xi, 262Xj\vfour{, + (of many variables) {\bf 262Fa}, 262Gb, 262I, 262Xg, 262Xi, 262Xj, +263Yf, \vfour{, 473B, 473Cd, 484N, 484Xh\vfive{, 534Xb, 565K}}; %4%5 {\it see also} derivative @@ -5613,7 +5648,7 @@ \vtwo{`differentiable relative to its domain' 222L, {\bf 262Fb}, 262I, 262M-262Q, %262M 262N 262O 262P 262Q 262Xd-262Xf, %262Xd 262Xe 262Xf -262Yc, 263D, 263Xc, 263Xd, 263Yc, 265E, 282Xk +262Yc, 263D, 263I, 263Xc, 263Xd, 263Yc, 265E, 282Xk }%2 \indexheader{differentiating} @@ -5624,7 +5659,7 @@ }%2 \indexheader{dilation} -\vtwo{dilation \S284 {\it notes}, {\bf 286C} +\vtwo{dilation 284Xd, \S284 {\it notes}, {\bf 286C} }%2 \vtwo{\indexheader{dimension}} @@ -5641,7 +5676,7 @@ \indexheader{Dirac} Dirac measure {\bf 112Bd}\vtwo{, - 257Xa, 274Lb, 284R, 284Xn, 284Xo, 285H, 285Xp\vfour{, + 257Xa, 274Lb, 284R, 284Xo, 284Xp, 285H, 285Xp\vfour{, {\it 417Xp}, 435Xb, 435Xd, 437S, 437Xr, 437Xt, 437Xu, 444Xq, {\it 478Xi}, {\it 482Xg}}}%2%4 @@ -5690,7 +5725,7 @@ \vthree{discrete topology ({\bf 3A3Ai})\vfour{, {\it 416Xb}, {\it 417Xi}, 436Xg, 439Cd, 439J, 442Ie, 443O, 445A, 445Xj, -449G, 449M, 449Xi, 449Xm-449Xp, %449Xm 449Xn 449Xo 449Xp +449G, 449M, {\it 449N}, 449Xj, 449Xn-449Xq, %449Xn 449Xo 449Xp 449Xq 4A2Ib, 4A2Qa}%4 }%3 @@ -5699,13 +5734,13 @@ }%5 \indexheader{disintegration} -disintegration of a measure 123Ye\vfour{, {\bf 452E}, +disintegration of a measure 123Ye\vfour{, {\it 443Q}, {\bf 452E}, 452F-452H, %452F 452G# 452H {\it 452K}, %# #="consistent" 452M, 452Xf-452Xh, %452Xf, 452Xg, 452Xh, 452Xk-452Xn, %452Xk 452Xl# 452Xm# 452Xn 452Xs, 452Xt, 453K, 453Xi, 453Ya, -455A, 455C, 455E, 455Oa, 455Pa, 455S, 455Xa, +455A, 455C, 455E, 455Oa, 455Pa, 455Xa, 455Xb, 455Xd, 459E, 459G, 459H, {\it 459K}, 459Xd, 459Ya, 477Xb, 478R, 479B, 479Yc, 495H\vfive{, 535Xl}; %5 @@ -5793,7 +5828,7 @@ \vthree{distributive laws in Riesz spaces 352E; {\it see also} weakly $\sigma$-distributive, weakly $(\sigma,\infty)$-distributive ({\bf 368N})\vfive{, weakly -$(\kappa,\infty)$-distributive ({\bf 511Xm})}%5 +$(\kappa,\infty)$-distributive ({\bf 511Xn})}%5 }%3 \vfive{\indexheader{distributivity} @@ -5803,7 +5838,7 @@ \indexheader{divergence} \vfour{divergence (of a vector field) {\bf 474B}, 474C-474E, %474C 474D 474E -475Nb, 475Xg, 484N +475Nc, 475Xg, 484N }%4 \vfour{Divergence Theorem 475N, 475Xg, 484N, 484Xh @@ -5916,7 +5951,7 @@ \indexheader{dual} \vfour{dual group (of a topological group) \S445 ({\bf 445A})\vfive{, - 561Xj}%5 + 561Xm}%5 }%4 %\vthree{dual linear operator {\it see} adjoint operator ({\bf 3A5Ed}) @@ -5931,7 +5966,7 @@ 356D, 356N, 356O, 356P, 356Xg, 356Yg, 365L, 365M, 366C, 366Dc, 369K, 3A5A, 3A5C, 3A5E-3A5H\vfour{, %3A5E 3A5F {\it 3A5G} 3A5H 436Ib, 437I, 4A4I\vfive{, - 561Xa, 561Xg}}}%4%5%3 + 561Xa, 561Xh}}}%4%5%3 }%2 \vfive{dual sequential composition (of supported relations) {\bf 512I}, @@ -6223,11 +6258,11 @@ 386D-386F, %386D, 386E 386F, 387C-387E, %387C, 387D, 387E, 387J, 387Xb, 388Yc\vfour{, - 494Xf, 494Xj, 494Yf}%4 + 494Xf, 494Xj}%4 }%3 \vthree{Ergodic Theorem 372D, 372F, 372J, 372Ya, 386Xc\vfour{, - 449Xq}; + 449Xr}; {\it see also} Maximal Ergodic Theorem (372C), Mean Ergodic Theorem (372Xa), Wiener's Dominated Ergodic Theorem (372Yb) }%3 @@ -6238,17 +6273,17 @@ \vfour{essential boundary {\bf 475B}, 475C, 475D, 475G, 475J-475L, %475J 475K 475L 475N-475Q, %475N 475O 475P 475Q -475Xb, 475Xc, 475Xg, 475Xh, 475Xj, 476Ee, 484Ra +475Xb, 475Xc, 475Xg, 475Xh, 475Xj, 475Yb, 476Ee, 484Ra }%4 essential boundary \vtwo{essential closure {\it 261Yj}, {\bf 266B}, 266Xa, 266Xb\vfour{, - {\bf 475B}, 475C, 475I, 475Xb, 475Xc, 475Xe, 475Xf, {\it 475Yg}, + {\bf 475B}, 475C, 475I, 475Xb, 475Xc, 475Xe, 475Xf, 475Yb, {\it 475Yg}, 478U, 479Pc, 484B, {\it 484K}, 484Ra, 484Ya}%4 }%2 \vfour{essential interior {\bf 475B}, 475C, {\it 475J}, -475Xb-475Xf, %475Xb 475Xc 475Xd 475Xe 475Xf -475Yg, 484Ra; +475Xb, 475Xd-475Xf, %475Xd 475Xe 475Xf +475Yb, 475Yg, 484Ra; {\it see also} lower Lebesgue density ({\bf 341E}) }%4 @@ -6258,7 +6293,7 @@ \vtwo{----- of a real-valued function {\bf 243D}, 243I, 255K\vthree{, {\it 376S}, {\it 376Xo}\vfour{, - 443Gb, 444R, {\it 492G}, {\it 492Xa}}}%4%3 + {\it 443Gb}, 444R, {\it 492G}, {\it 492Xa}}}%4%3 }%2 \indexheader{essentially} @@ -6284,13 +6319,13 @@ %Ev \indexheader{even} -\vtwo{even function 255Xb, 283Yb, 283Yc +\vtwo{even function 255Xb, 283Yc, 283Yd }%2 %Ew%Ex \indexheader{exchangeable} -\vtwo{exchangeable family of random variables {\bf 276Xe}\vfour{, +\vtwo{exchangeable family of random variables {\bf 276Xg}\vfour{, {\bf 459C}, 459Xa, 459Xb}%4 }%2 @@ -6325,8 +6360,11 @@ ({\bf 477Ia}) }%4 -\vtwo{\indexheader{expectation}} -\vtwo{expectation of a random variable {\bf 271Ab}, 271E, 271F, 271I, +\indexiiheader{expectation} +\vtwo{expectation (of a distribution) {\bf 271F}\vfour{, 455Xj, 455Yc}%4 +}%2 + +\vtwo{----- (of a random variable) {\bf 271Ab}, 271E, 271F, 271I, {\it 271Xa}, 271Ye, 272R, 272Xb, {\it 272Xi}, 274Xb, 285Ga, {\it 285Xo}, 285Xt; {\it see also} conditional expectation ({\bf 233D}) @@ -6358,7 +6396,7 @@ extension of finitely additive functionals 113Yi\vthree{, 391G, 391Ye\vfour{, - 413K, 413N, 413Q, 413S, 413Yd, 449N, 449O, 449Xn, 449Yg, + 413K, 413N, 413Q, 413S, 413Yd, 449N, 449O, 449Xo, 449Yg, 454C-454F, %454C 454D 454E 454F {\it 454Xa}, 457A, 457C, 457D, 457Xb-457Xe, %{\it 457Xb} 457Xc 457Xd 457Xe @@ -6379,9 +6417,9 @@ 432D, 432F, {\it 432Ya}, 433J, 433K, {\it 434A}, {\it 434Ha}, {\it 434Ib}, 434R, 435B, 435C, 435Xa-435Xd, %435Xa 435Xb 435Xc 435Xd 435Xg, 435Xj, 435Xo, {\it 439A}, {\it 439M}, {\it 439O}, 439Xk, -441Ym, 449O, 455H, 455J, 455Yd, +441Ym, {\it 449O}, 455H, 455J, 455Yd, 457E, 457G, {\it 457Hc}, {\it 457J}, -457Xa, 457Xg, 457Xi, {\it 457Xn}, +457Xa, 457Xh, 457Xi, {\it 457Xn}, {\it 457Yc}, 464D, {\it 466H}, 466Xd, {\it 466Za}\vfive{, 538I-538K, %538I 538J 538K @@ -6437,7 +6475,7 @@ }%2 \indexivheader{faithful} -\vfour{faithful action 449De, {\bf 4A5Be} +\vfour{faithful action 449De, {\bf 4A5Be} }%4 \vfour{faithful representation {\bf 446A}, 446N @@ -6474,7 +6512,7 @@ \indexheader{Federer} \vfour{Federer exterior normal {\bf 474O}, 474P, 474R, -475N, 475Xd, 475Xg, 484N, 484Xh; +475Nb, 475Xd, 475Xg, 484N, 484Xh; {\it see also} canonical outward-normal function ({\bf 474G}) }%4 @@ -6554,7 +6592,7 @@ \indexiiheader{filtration} \vtwo{filtration (of $\sigma$-algebras) {\bf 275A}\vfour{, - {\bf 455L}, {\it 478Vb}}%4 + {\bf 455L}, 455O, 455T, 477Hc, {\it 478Vb}}%4 }%2 \vfive{----- {\it see also} tight filtration ({\bf 511Di}) @@ -6578,19 +6616,20 @@ }%3 }%2 -\vfour{finite-dimensional linear space 4A4Bi, 4A4J +\vfour{finite-dimensional linear space 4A4Bi, 4A4Je }%4 \vfour{finite-dimensional representation {\bf 446A}, 446B, 446C, 446N, -446Xa, 446Xb, 446Ya, 446Yb +446Xa, 446Ya, 446Yb }%4 \vthree{finite intersection property {\bf 3A3D}\vfour{, 4A1Ia}%4 }%3 -\vfour{finite perimeter (for sets in $\BbbR^r$) {\bf 474D}, 474Xc, -475Mb, 475Q, 475Yd, 484B, 484Xh +\vfour{finite perimeter (for sets in $\BbbR^r$) 474Xb, 474Xc, +475Mb, 475Q, 475Xk, 475Xl, 484B, 484Xh; + {\it see also} locally finite perimeter ({\bf 474D}) }%4 \vthree{finite rank operators @@ -6616,11 +6655,11 @@ 327C, 363Lf\vfour{, 413H, 413K, 413N, 413P, 413Q, 413S, 413Xh, 413Xm, 413Xn, 413Xq, 416O, 416Q, -416Xm, 416Xn, 416Xs, 449J, 449L, -449Xl, 449Xn-449Xp, %449Xn 449Xo 449Xp +416Xm, 416Xn, 416Xs, 449J, 449L, {\it 449O}, +449Xm, 449Xo-449Xq, %449Xo 449Xp 449Xq 449Yg, 449Yh, 457A-457D, %457A 457B 457C 457D -457Ha, {\it 457Ib}, 457Xg, 457Xi, 471Qa, +457Ha, {\it 457Ib}, 457Xh, 457Xi, 471Qa, {\it 482H}, {\it 493C}}}; %3%4 {\it see also} countably additive\vthree{, completely additive} }%2 fin add fnal @@ -6637,10 +6676,10 @@ ({\bf 326Ye}), 326Yl-326Yn, %326Yl, 326Ym, 326Yn, 326Yq, 326Yr, 327B, 327C, 331B, {\bf 361B}, 361Xa-361Xc, %361Xa 361Xb 361Xc -361Ye, 362A, 363D, 363E, 363L, 364Xj, 365E, 366Ye, 373H, +361Xl, 361Ye, 362A, 363D, 363E, 363L, 364Xj, 365E, 366Ye, 373H, 391D-391G, %391D 391E 391F 391G 391I, 391J, 392Hd, 392Kg, 392Ye, 395N, 395O\vfour{, - 413Xp, 416Q, 457Xh, 481Xh, 491Xu\vfive{, + 413Xp, 416Q, 457Xg, 481Xh, 491Xu\vfive{, 538Xh, 538Yp, 553K, 553Xc, 567J, 567Yf}}; %4%5 {\it see also} chargeable Boolean algebra ({\bf 391X}), completely additive functional ({\bf 326N}), @@ -6677,7 +6716,7 @@ \vfour{First Separation Theorem (of descriptive set theory) 422I, 422Xd, 422Yc\vfive{, - 562Ya}%5 + 562Fa}%5 }%4 \vthree{\indexheader{fixed}} @@ -6703,7 +6742,7 @@ }%4 \indexivheader{F{\o}lner} -\vfour{F{\o}lner sequence {\bf 449Xm}, 449Ye +\vfour{F{\o}lner sequence {\bf 449Xn}, 449Ye }%4 \indexvheader{forcing} @@ -6749,7 +6788,7 @@ \indexheader{Fourier} \vtwo{Fourier coefficients {\bf 282Aa}, 282B, 282Cb, 282F, 282Ic, 282J, -282M, 282Q, 282R, 282Xa, 282Xg, 282Xq, 282Xt, 282Ya, 283Xu, 284Ya, 284Yg +282M, 282Q, 282R, 282Xa, 282Xg, 282Xq, 282Xt, 282Ya, 283Xt, 284Ya, 284Yg }%2 \vtwo{Fourier's integral formula {\bf 283Xm} @@ -6769,7 +6808,7 @@ }%2 includes `representatives' \vtwo{Fourier-Stieltjes transform\vfour{ {\bf 445C}, 445D, 445Ec, -445Xb, 445Xc, 445Xo, 445Yf, 466J, 479H;} %4 +445Xb, 445Xc, 445Xf, 445Xo, 445Xq, 445Yf, 445Yh, {\it 466J}, 479H;} %4 {\it see\vfour{ also}} characteristic function ({\bf 285A}) }%2 @@ -6831,7 +6870,7 @@ }%5 \vfive{Freese-Nation number of a pre- or partially ordered set {\bf 511Bi}, -511Dh, 511Hc, 511Xi, 511Xj, 511Yb, 518A, 518B, 518D, 518G, 518Xb, 518Xd, +511Dh, 511Hc, 511Xk, 511Xl, 511Yb, 518A, 518B, 518D, 518G, 518Xb, 518Xd, 518Xf, 518Ya, 518Yc; {\it see also} regular Freese-Nation number ({\bf 511Bi}) }%5 @@ -6895,7 +6934,7 @@ full outer measure {\bf 132F}, 132Yd, 134D, 134Yt\vtwo{, 212Eb, 214F, 214J, 234F, 234Xa, 241Yg, 243Ya, 254Yf\vthree{, 322Jb, 324A, {\it 343Xa}\vfour{, - {\it 415J}, 415Qc, 419Xd, 432G, 439Fa, 443Ym, {\it 456H}, + {\it 415J}, 415Qc, 419Xd, 432G, 439Fa, 443Yq, {\it 456H}, {\it 495G}, 495Nc\vfive{, 521Jc, 521Xd, 521Xl, 523D, 524Xh, 527Xa, 537M}; %5 full outer Haar measure {\bf 443Ac}, 443K @@ -6910,7 +6949,7 @@ 383C, 383Xl, 388A-388C, %388A 388B 388C 388G, 388H, 388J-388L, %388J 388K 388L 388Ya, 395Xi\vfour{, - 494C, 494G, 494H, 494L-494O, %494L, 494M 494N, 494O, + 494Cg, 494G, 494H, 494L-494O, %494L, 494M 494N, 494O, 494Q, 494R, 494Xe, 494Yi\vfive{, 556N, 566Rb, 566Xh, 566Xi}}; %4%5 {\it see also} countably full ({\bf 381Bf}), finitely full ({\bf 381Xi}) @@ -6934,7 +6973,7 @@ }%3 \indexheader{function} -function 1A1B\vfive{, 5A3Eb, 5A3H}%5 +function 1A1B\vfive{, 5A3Eb, 5A3H, {\it 5A3Kb}}%5 \vthree{function space {\it see} Banach function space (\S369) }%3 @@ -6966,7 +7005,7 @@ 512Xg, 513E, 513Ie, 513Xa, 513Xi, 514Ha, 514Na, 514Xa, 516C, 517Ya, 521Fa, 521Ja, 522N, 522Yg, 523Xa, 523Xc, 524C-524E, %524C 524D 524E -524G, 524Sb, 526F, 534Bc, 539Ca; +524G, 524Tb, 526F, 534Bc, 539Ca; {\it see also} Tukey function ({\bf 513D}) }%5 % Galois-Tukey connection \prGT @@ -7025,14 +7064,14 @@ }%4 \indexheader{Gaussian} -\vtwo{Gaussian distribution\vfour{ \S456 ({\bf 456A}), 477D, 477Yf, 477Yg, -494F;} +\vtwo{Gaussian distribution\vfour{ \S456 ({\bf 456A}), 466Xp, +477D, 477Yf, 477Yg, 494F;} {\it see\vfour{ also}} standard normal distribution ({\bf 274Aa}) }%2 \vfour{Gaussian measure {\bf $\pmb{>}$466N}, 466O, -466Xo-466Xr, %466Xo 466Xp 466Xq 466Xr -466Yc, 477Yj +466Xm-466Xp, %466Xm 466Xn 466Xo 466Xp +466Ye, 477Yj }%4 \vfour{Gaussian process {\bf 456D}, 456E, 456F, 456Ya, @@ -7049,7 +7088,7 @@ \vfive{\indexheader{generalized} generalized continuum hypothesis 513J, {\it 518K}, -523P, 524Q, 525P, {\it 553Z}, 555Q, 555Xc, {\bf 5A6A} +523P, 524R, 525O, {\it 553Z}, 555Q, 555Xc, {\bf 5A6A} }%5 \indexheader{generated} @@ -7131,7 +7170,7 @@ \indexheader{gradient} \vfour{gradient (of a scalar field) {\bf 473B}, 473C, 473Dd, 473H-473L, %473H 473I 473J 473K 473L -474Bb, 474K, {\it 474Q}, 475Xm, 476Yb, 479T, 479U +474Bb, 474K, {\it 474Q}, 475Xl, 476Yb, 479T, 479U }%4 \indexheader{graph} @@ -7142,7 +7181,9 @@ \vfour{greatest ambit (of a topological group) {\bf 449D}, 449E, 493Be }%4 -\indexheader{Green} +\indexivheader{Green} +\vfour{Green's second identity 475Xn}%4 + \vfour{Green's theorem {\it see} Divergence Theorem (475N) }%4 @@ -7166,7 +7207,7 @@ }%3 \vfour{group homomorphism 442Xi, {\it 445Xe}, 451Yt, 494Ob, 4A5Fa, -4A5L\vfive{, +4A5La\vfive{, 567H}%5 }%4 @@ -7174,7 +7215,7 @@ \vfive{groupwise dense family of sets {\bf 5A6Ib} }%5 -\vfive{groupwise density number 5A3Yl, {\bf 5A6Ib}, 5A6J +\vfive{groupwise density number 538Yn, {\bf 5A6Ib}, 5A6J }% %Gs%Gt%Gu%Gv%Gw%Gx%Gy%Gz @@ -7187,13 +7228,14 @@ \vfour{Haar measurable envelope {\bf 443Ab}, 443Xf, 443Xm }%4 -\vfour{Haar measurable function {\bf 443Ae}, 443G, {\it 444Xp}, 451Yt +\vfour{Haar measurable function {\bf 443Ae}, {\it 443G}, {\it 444Xp}, +451Yt }%4 \vfour{Haar measurable set {\bf 442H}, 442Xd, 443A, 443D, 443F, -443Jb, 443Qc, {\it 443Yn}, 444L, 447Aa, 447B, +443Jb, 443Qc, {\it 443Yo}, 444L, 447Aa, 447B, 447D-447H, %447D 447E 447F 447G 447H -449I, 449J +449J }%4 \vfour{Haar measure chap.\ 44 ({\bf 441D}), 452Xj, 465Yi, 491H, 491Xl, @@ -7207,8 +7249,8 @@ }%4 \vfour{Haar negligible set {\bf 442H}, 443Aa, 443F, 443Jb, 443Qc, -443Xn, 443Yn, 444L, 444Xm, 444Xn, 444Ye, 444Yf, -449I, 449J +443Xn, 443Yo, 444L, 444Xm, 444Xn, 444Ye, 444Yf, +449J }%4 \vfour{Haar null set {\bf 444Ye} @@ -7218,7 +7260,7 @@ \vthree{Hahn-Banach theorem 233Yf, 363R, {\it 368Xb}, 373Yd, 3A5A, 3A5C\vfour{, 4A4D, 4A4E\vfive{, - 561Xg}}%4%5 + 561Xh}}%4%5 }%3 \vtwo{Hahn decomposition (for countably additive functionals) 231E @@ -7254,7 +7296,7 @@ (in general totally ordered spaces) {\bf 4A2A}}%4 \vtwo{half-space (in $\BbbR^r$) 285Xl\vfour{, -466Xj, 474I, 474Xc, 475Xk, {\it 476D}}%4 +466Xi, 474I, 474Xc, {\it 476D}}%4 }%2 \indexiiiheader{Hall} @@ -7316,10 +7358,12 @@ \vfour{Hausdorff gap {\bf 439Yk} }%4 -\vtwo{Hausdorff measure \S264 ({\bf 264C}, {\bf 264Db}, {\bf 264K}, {\bf 264Yo}), 265Yb\vthree{, +\vtwo{Hausdorff measure \S264 +({\bf 264C}, {\bf 264Db}, {\bf 264K}, {\bf 264Yo}), +265Xd, 265Yb\vthree{, 343Ye, {\it 345Xb}, {\it 345Xg}\vfour{, 411Yb, 439H, 439Xl, 441Yc-441Ye, %441Yc 441Yd 441Ye -441Yg, 442Ya, 443Yq, 456Xb, +441Yg, 442Ya, 443Ys, 456Xb, \S471 ({\bf 471A}, {\bf 471Ya}), 476I, 477L, 479Q\vfive{, 534B, 534Yb, 534Yc, 534Za, 537Xf, 565O}}}; %3%4%5 {\it see also} normalized Hausdorff measure ({\bf 265A}) @@ -7426,9 +7470,9 @@ \indexheader{Hilbert} \vtwo{Hilbert space 244Na, 244Yk\vthree{, 366Mc, {\bf 3A5M}\vfour{, - 456C, 456J, 456Xe, 456Xh, 456Yb, 466Xk, 493Xe, 493Xg, 495Xh, + 456C, 456J, 456Xe, 456Xh, 456Yb, 466Xj, 493Xf, 493Xg, 495Xh, 4A4K, 4A4M\vfive{, - 561Xo, 564Xc, 566P}}; %4%5 + 561Xr, 564Xc, 566P}}; %4%5 {\it see also} inner product space ({\bf 3A5M})}%3 }%2 @@ -7484,9 +7528,8 @@ }%3 homogeneous B alg \vthree{----- measure algebra 331N, 331Xk, 332M, 344Xe, -373Yb, 374H, 374Yc, 375Lb, 383E, 383F, 383I, 395R\vfour{, - 494I, 494J\vfive{, - 528Da, 528Ya, 529D}}; %4%5 +373Yb, 374H, 374Yc, 375Lb, 383E, 383F, 383I, 395R\vfive{, + 528Da, 528Ya, 529D}; %5 {\it see also} quasi-homogeneous ({\bf 374G}) }%3 homogeneous m alg @@ -7495,7 +7538,7 @@ }%3 \vthree{----- probability algebra 333P, 333Yc, 372Xn, 385Sb\vfour{, -494Eb, 494Xi}%4 +494Eb, 494I, 494J, 494Xi}%4 }%3 \indexheader{homomorphic} @@ -7581,9 +7624,9 @@ \vtwo{\indexheader{identically}} \vtwo{identically distributed random variables {\bf 273I}, 273Xi, -274I, 274Xj, 276Xf, 276Yg, 285Xn, 285Yc\vthree{, +274I, 274Xj, 276Xd, 276Yg, 285Xn, 285Yc\vthree{, 372Xg}; %3 - {\it see also} exchangeable sequence ({\bf 276Xe}\vfour{, {\bf 459C}}) + {\it see also} exchangeable sequence ({\bf 276Xg}\vfour{, {\bf 459C}}) }%2 %Ie%If%Ig%Ih%Ii%Ij%Ik%Il%Im @@ -7605,8 +7648,9 @@ 418Xo, 418Xs, 418Yf, 432G, 433D, 434Yp, 437Jh, 437N, {\it 437Xm}, {\it 437Yo}, 437Yu, 443Qd, 441Xk, 444Xa, 451O, 451P, 451S, 451Xh, -{\it 452T}, 454J, 456B, 456Xb, 455A, 455Ea, 455Xd, 455Xf, 461B, 461Xq, -462H, 466Xo, 466Xq, 474H, 479Xj, 479Xk, 491Ea\vfive{, +{\it 452T}, 454J, 456B, 456Xb, 455A, 455Ea, 455Sb, +455Xd, 455Xf, 461B, 461Xq, +462H, 466Xm, 474H, 479Xj, 479Xk, 491Ea\vfive{, 521Fb, 521Ya, {\it 524Xe}, 533Xb, 533Xd, {\it 538Xy}, 543Ba, 563Ka, 563Xa}}}%3%4%5 }%2 image measure @@ -7673,14 +7717,14 @@ 234Xh-234Xk, % 234Xh 234Xi 234Xj 234Xk 234Yi, 234Yj, 234Yl-234Yn, %234Yl 234Ym 234Yn 235K, {\it 235N}, 235Xh, 235Xl, 235Xm, -253I, 256E, 256J, 256L, 256Xe, 256Yd, 257F, 257Xe, 263Ya, 275Yj, 275Yk, +253I, 256E, 256J, 256L, 256Xe, 256Yd, 257F, 257Xe, 263Ya, 275Yj, 275Yk, 285Dd, 285Xe, 285Ya\vthree{, 322K, 342Xd, 342Xn, {\it 365T}\vfour{, 412Q, 414H, 414Xe, 415O, 416S, 416Xu, 416Yf, 441Yo, 442L, 444K, 444P, 444Q, {\it 445F}, 445Q, 451Xc, 451Yj, 452Xf, 452Xh, 453Xe, 465Cj, 471F, 476A, 476Xa, 491R, 491Xr\vfive{, - 511Xe, 533Xb, 538Xk}}}; + 511Xf, 533Xb, 538Xk}}}; {\it see also} uncompleted indefinite-integral measure }%2 indefinite-integral measure @@ -7693,8 +7737,10 @@ \vtwo{\indexheader{independent}} \vthree{independent family in a probability algebra {\bf 325Xf}, 325Yg, -371Yc, 376Yd\vfive{, - 553G}%5 +371Yc, 376Yd\vfour{, + {\bf 458L}, 464Qb\vfive{, + 553G}; {\it see also}\vfive{ Boolean-independent ({\bf 515Aa}),} +relatively independent ({\bf 458L})}%4 }%3 \vthree{independent family in $L^0(\frak A)$ {\bf 364Xe}, 364Xf, 364Xs, @@ -7726,8 +7772,7 @@ }%2 independent random variables \vtwo{independent sets {\bf 272Aa}, {\it 272Bb}, 272F, 272N, 273F, -273K, 273Xo\vfour{, - {\it 464Qb}}%4 +273K, 273Xo }%2 \vthree{independent subalgebras of a probability algebra {\bf 325L}, @@ -7735,9 +7780,11 @@ {\it 327Xe}, 364Xe, 385Q, 385Sf, {\it 385Xd-385Xf}, %{\it 385Xd}{\it 385Xe}{\it 385Xf}, 387B\vfour{, - 495J, 497Xa\vfive{, + {\bf 458L}, 495J, 497Xa\vfive{, 526D, 556La}}; %4%5 - {\it see also} Boolean-independent ({\bf 315Xp}\vfive{, {\bf 515A}}) + {\it see also} Boolean-independent +({\bf 315Xp}\vfive{, {\bf 515A}})\vfour{, +relatively independent ({\bf 458L})}%4 }%3 \vtwo{independent $\sigma$-algebras {\bf 272Ab}, 272B, 272D, 272F, 272J, @@ -7840,7 +7887,7 @@ }%3 inner measure 113Yg\vtwo{, - 212Ya, 213Xe, 213Yc\vfour{, + 212Ya, 213Yd\vfour{, {\bf 413A}, 413C, 413Xa-413Xc, %{\it 413Xa} 413Xb 413Xc 413Ya}%4 }%2 @@ -7849,14 +7896,14 @@ 213Xe\vfour{, {\bf 413D}, 413E, 413F, 413Xd-413Xg, %413Xd 413Xe 413Xf 413Xg 413Yb, {\it 413Yg}, 417A, 417Xa, 418Xs, 431Xe, 443Xb, -451Pb, 457Xg, {\it 463I}}} %2%4 +451Pb, 457Xi, {\it 463I}}} %2%4 % inner measure \vtwo{inner product space 244N, 244Yn, 253Xe\vthree{, 377Xb, {\bf 3A5M}\vfour{, 456Xe, 476D, 476E, 476I-476L, %476I 476J 476K 476L 476Xd-476Xf, %476Xd 476Xe 476Xf -493F, 493G, 493Xd, 4A4J\vfive{, +493F, 493G, 493Xd, 493Xe, 4A4J\vfive{, 566Yd}}; {\it see also} Hilbert space ({\bf 3A5M}) }%3 @@ -7876,10 +7923,10 @@ 413M, 413O, 413Sb, 413Xi, 413Xk, 414Mb, 414Xg, 416Yb, 416Yc, 417A, 417Ye-417Yg, %417Ye 417Yf 417Yg 418Yi, 418Yj, 424Yf, 431Xb, 434L, {\it 434Yh}, {\it 443L}, {\it 443O}, -{\it 443Yg}, 451Ka, +{\it 443Yk}, 451Ka, 451Xj, {\it 452H}, {\it 452I}, {\it 452M}, {\it 452Xd}, 454A, 454Q, 454Yd, 462J, {\it 462Yc}, 463Yd, {\it 465Xf}, 467Xj, 475F, -475I, 475Yc\vfive{, +475I, 475Yd\vfive{, 532Hb, 533A, 533Ca, 533D, 533Xa, 535K, {\it 538I}, 566D, 566I}}%4%5 }%3 }%2 @@ -7893,7 +7940,7 @@ 417Xk, 417Xl, 417Xn, 417Xs, 417Xw, 417Yb, 417Yd, 419J, 432Ya, 433A, 433Xa, 434Yf\vfive{, - 535Eb, 535Xm}%5 + {\it 532Ec}, 535Eb, 535Xm}%5 }%4 \vtwo{----- ----- with respect to closed sets 134Xe, @@ -7907,10 +7954,10 @@ 418Yo, 419A, 431Xb, 432D, 432G, 432Xc, 432Xf, 433E, 434A, {\it 434Ga}, {\it 434Ha}, 434M, 434Yb, 434Yn, 435C, 435Xm, 435Xo, 438F, -452Yf, 454Q, 454Yd, 457M, 457Ye, {\it 466H}, +452Yf, 454Q, 454Yd, 457M, {\it 466H}, 471De, 471Xh, 471Yb, 476Aa, 476Xa, 482F, {\it 482G}, 482Xd, 491Yn\vfive{, - 563F, 563Xd}; %5 + 521Xn, 563F, 563Xd}; %5 {\it see also} quasi-Radon measure ({\bf 411Ha})}}%4%3 }%2 inner regular with respect to closed sets @@ -7960,7 +8007,7 @@ \vthree{----- with respect to an additive functional ($\dashint$) {\bf 363L}, 364Xj\vfour{, 413Xh, {\it 437B}, {\it 437D}, 437I-437K, %{\it 437I} 437J 437Ka -{\it 437Xs}, 437Yg, 449Xn, 481Xh, 482Xm\vfive{, +{\it 437Xs}, 437Yg, 449Xo, 481Xh, 482Xm\vfive{, 538P-538R, %538P, 538Q, 538R, 538Xq, 538Xs, 538Yg, 538Yo}}%4 %5 }%3 \dashint ="horizontal integral" @@ -8002,16 +8049,17 @@ }%4 \indexvheader{interpretation} -\vfive{interpretation of Borel codes {\bf 562A}, 562B, 562G, 562H, -562K-562M, %562K 562L 562Mb -562P, 562R, {\bf 562T} +\vfive{interpretation of Borel codes {\bf 562B}, 562C, 562I, 562J, +562M-562O, %562M 562N 562Ob +562R, 562T, {\bf 562V} }%5 \indexheader{intersection} \vthree{intersection number (of a family in a Boolean algebra) {\bf 391H}, 391I-391K, %391I, 391J, 391K, -391Xi, 391Xj, 391Yd, 392E, 393Yh\vfive{, - 525Xh, 538Yh} +391Xi, 391Xj, 391Yd, 392E, 393Yh\vfour{, + {\it 457 notes}\vfive{, + 525Xg, 538Yh}} %4%5 }%3 \indexheader{interval} @@ -8029,8 +8077,8 @@ \vthree{----- additive function 395N-395P, %395N 395O 395P 395Xd, 395Xe, 395Z, 396B, 396Xc\vfour{, - 449J, 449L, 449Xl, 449Xn-449Xp, %449Xn 449Xo 449Xp -449Yg, 449Yh, 449Yj\vfive{, + 449J, 449L, 449Xm, 449Xo-449Xq, %449Xo 449Xp 449Xq +449Yg, 449Yh, {\it 449Yj}\vfive{, 556P}}%4%5 }%3 @@ -8043,7 +8091,7 @@ \vthree{----- lower density 346Xb }%3 -\vfour{----- mean 449E, 449H, 449J, 449Xf, 449Yc; +\vfour{----- mean 449E, 449H, 449J, 449Xg, 449Yc; {\it see also} two-sided invariant mean }%4 @@ -8053,7 +8101,7 @@ 441Xk, 441Xs, 441Xt, 441Yb, 441Yf, 441Yk-441Yn, %441Yk 441Yl 441Ym 441Yn 441Yp, 441Yq, 442Ya, 442Z, 443Q, 443R, 443U, 443Xq, 443Xs, {\it 443Xu}, 443Xy, -447E, 448P, 448Xf, 448Xi, 448Xk, 449A, 449E, 452T, 456Xc, +447E, 448P, 448Xe, 448Xh, 448Xj, 449A, 449E, 452T, 456Xc, 461Q, 461R, 461Xl, 461Xn, 461Xo, 461Ye, 476C, 476E, 476I, 476Ya\vfive{, 544Xi}; %5 @@ -8073,38 +8121,40 @@ \vthree{inverse (of an element in an $f$-algebra) 353Pc }%3 -\vtwo{inverse Fourier transform {\bf 283Ab}, 283B, {\bf 283Wa}, 283Xb, {\bf 284I}\vfour{, +\vtwo{inverse Fourier transform {\bf 283Ab}, 283B, {\bf 283Wa}, 283Xb, +{\bf 284I}\vfour{, 445P, 445Yg}; {\it see also} Fourier transform }%2 inverse image (of a set under a function or relation) {\bf 1A1B} +\indexheader{inverse-measure-preserving} \allowmorestretch{468}{ inverse-measure-preserving function 134Yl-134Yn\vtwo{, %134Yl 134Ym 134Yn {\bf 234A}, 234B, 234Ea, 234F, 234Xa, 235G, 235Xm, 241Xg, 242Xd, 243Xn, 244Xo, 246Xf, 251L, 251Wp, 251Yb, 254G, 254H, 254Ka, 254O, 254Xc-254Xf, %254Xc 254Xd 254Xe 254Xf -254Xh, 254Yb, 256Yf\vthree{, +254Xh, 254Yb, 254Yh, 256Yf\vthree{, 324M, 324N, 328Xb, 341P, 341Xe, 341Yc, 341Yd, 343C, {\it 343J}, 343Xd, 343Xi, 343Yd, 365Xi, 372H-372K, %372H 372I 372J 372K 372Xe, 372Xf, 372Yf, 372Yj, 385S-385V, %{\it 385S} 385T 385U 385V 386Xb\vfour{, 411Ne, 412K, 412M, 413Eh, 413T, -{\it 413Yc}, 414Xa, 414Xq, 414Xs, 416W, 417Xg, 418Hb, +{\it 413Yc}, 414Xa, 414Xq, 414Xs, 416W, 416Yi, 417Xg, 418Hb, 418M, 418P, 418Q, 418Xf, 418Xg, 418Xn, 418Xr, 418Xs, 418Yl, 419L, 419Xf, 432G, 433L, 433Xd, 433Yd, 435Xl, 435Xm, 436Xr, 437T, 438Xe, 438Xf, 441Xa, 442Xa, 443L, 451E, 452E, 452I, 452O-452R, %452O 452P 452Q 452R -452Xl, 452Xm, 452Yb, 453K, {\it 454G}, 454J, {\it 454M}, -456Ba, 456Ib, 456K, 456Yb, 455S, 455T, 455Xb, 455Xd, 455Xk, 457F, +452Xl, 452Xm, 452Yb, 453K, {\it 454G}, 454J, {\it 454M}, 455Sc, +456Ba, 456Ib, 456K, 456Yb, 455S, 455U, 455Xb, 455Xd, 455Xk, 457F, {\it 457Hb}, 457Xf, 457Xj-457Xm, %457Xj 457Xk 457Xl 457Xm 457Yd, 457Za, 457Zb, {\it 458Qb}, 458Xs, {\it 459I}, {\it 459J}, 461Qb, 461R, 461Xn-461Xp, %461Xn 461Xo 461Xp -461Yd, 461Ye, 464B, {\it 465Xe}, 466Xq, 477E, +461Yd, 461Ye, 464B, {\it 465Xe}, 466Xp, 477E, 477G, {\it 477Yg}, 491Ea, 495G, 495I, 495Xe, 495Xi\vfive{, - 521Fa, 535P, 535Yc, 537Bb, 538Jb, 538Xw, 543G, 564M}}; %5%4 + 521Fa, 521Xn, 535P, 535Yc, 537Bb, 538Jb, 538Xw, 543G, 564M}}; %5%4 isomorphic \imp\ functions {\bf 385Tb}}; %3 {\it see also }\vthree{almost isomorphic ({\bf 385U}), ergodic \imp\ function ({\bf 372Ob}), }%3 @@ -8116,7 +8166,8 @@ \indexheader{inversion} \vtwo{Inversion Theorem (for Fourier series and transforms) 282G-282J, %282G, 282H, 282I, 282J -282L, 282O, 282P, 283I, 283L, 284C, 284M\vfour{, +282L, 282O, 282P, 283F, 283I, 283J, 283L, 283Wc, 283Wk, 283Xm, +284C, 284M\vfour{, 445P}; {\it see also} Carleson's theorem }%2 @@ -8170,14 +8221,15 @@ \vthree{\indexheader{isometry}} \vthree{isometry 324Yg, {\bf 3A4Ff}, 3A4G\vfour{, - 441Xm, 448Xf, 448Xi, 474C, 474H, 476J, 476Xd, {\it 493Xg}, 4A4J}%4 + 441Xm, 448Xe, 448Xh, 474C, 474H, 476J, 476Xd, {\it 493Xg}, 4A4J}%4 }%3 \vfour{----- group (of a metric space) {\bf 441F}, 441G, 441H, 441Xn-441Xs, %441Xn 441Xo 441Xp 441Xq 441Xr 441Xs -441Ya, 441Yh, 441Yj, 441Yk, 443Xw, 443Xy, 443Yq, -448Xk, 449Xc, 449Xg, 476C, 476I, 476Xd, 476Ya, -493G, 493Xb, 493Xd, 493Xe, 494Xa, 494Xl +441Ya, 441Yh, 441Yj, 441Yk, 443Xw, 443Xy, 443Ys, +448Xj, 449Xc, 449Xh, 476C, 476I, 476Xd, 476Ya, +493G, 493Xb, 493Xd-493Xf, %493Xd, 493Xe, 493Xf, +494Xa, 494Xl }%4 \vthree{\indexheader{isomorphic}} @@ -8247,7 +8299,7 @@ \indexivheader{Kadec} \vfour{Kadec norm {\bf 466C}, 466D-466F, %466D 466E 466F -{\it 466Ye}, 467B +{\it 466Yb}, 467B }%4 \vfour{Kadec-Klee norm {\it see} Kadec norm ({\bf 466C}) @@ -8255,7 +8307,7 @@ \indexiiiheader{Kakutani} \vthree{Kakutani's theorem 369E, {\it 369Yb}\vfive{, - 561H}; %5 + 561Hb}; %5 {\it see also} Halmos-Rokhlin-Kakutani lemma (386C) }%3 @@ -8269,8 +8321,7 @@ \indexivheader{Kantorovich} \vfour{Kantorovich-Rubinstein metric {\bf 437Qb}, 437R, 437Xs, -437Yo, 437Yv, 438Yl, -{\it 457K}, {\bf 457Ld}, {\it 457Xo} +437Yo, 437Yv, 438Yl, {\it 457K} }%4 \rhoKR \indexheader{Kawada} @@ -8324,7 +8375,7 @@ \vfive{\indexvheader{Knaster}} \vfive{Knaster's condition (for a pre-ordered set, topological space, -Boolean algebra) {\bf 511Ef}, 516U, 517O, 517S, 525Ub, 527Yd, 539Jc, 553Xd +Boolean algebra) {\bf 511Ef}, 516U, 517O, 517S, 525Tb, 527Yd, 539Jc, 553Xd }%5 %Ko @@ -8364,7 +8415,7 @@ \vfour{\Krein's theorem 461J }%4 -\vfour{\Krein-Mil'man theorem 4A4Gb\vfive{, 561Xg}%5 +\vfour{\Krein-Mil'man theorem 4A4Gb\vfive{, 561Xh}%5 }%4 \indexheader{Kronecker} @@ -8409,6 +8460,10 @@ 479T }%4 +\indexivheader{last} +\vfour{last exit time 479Xt +}%4 + \indexheader{laterally} \vthree{laterally complete Riesz space {\bf 368L}, 368M }%3 @@ -8463,7 +8518,7 @@ }%3 \vtwo{Lebesgue's Density Theorem \S223, 261C, {\it 275Xg}\vfour{, - 447D, 447Xc, 471P, {\it 475Yc}; + 447D, 447Xc, 471P; {\it see also} Besicovitch's Density Theorem (472D) }%4 }%2 @@ -8484,22 +8539,23 @@ Lebesgue measurable function {\bf 121C}, 121D, 134Xg, 134Xj\vtwo{, {\it 225H}, 233Yd, 262K, 262P, 262Yc\vfour{, - 466Xh, 483Ba, 484Hd}%4 + 466Xk, 483Ba, 484Hd}%4 }%2 Lebesgue measurable set {\bf 114E}, 114F, 114G, {\it 114Xe}, 114Ye, {\bf -115E}, 115F, 115G\vfour{, +115E}, 115F, 115G\vtwo{, 225Gb\vfour{, {\it 419Xe}\vfive{, - {\bf 565D}, 565E, 565Xa, 567O}}%4%5 + {\bf 565D}, 565E, 565Xa, 567O}}}%2%4%5 Lebesgue measure (on $\Bbb R$) \S114 ({\bf 114E}), 131Xb, 133Xd, 133Xe, 134G-134L\vtwo{, %134G 134H 134I 134J 134K 134L - 212Xc, {\it 216A}, chap.~22, 242Xi, 246Yd, 246Ye, {\it 252N}, {\it 252O}, + 212Xc, {\it 216A}, chap.\ 22, 242Xi, 246Yd, 246Ye, +{\it 252N}, {\it 252O}, {\it 252Xf}, {\it 252Xg}, {\it 252Ye}, {\it 252Yo}, \S255\vthree{, {\it 342Xo}, 343H, 344Kb, 345Xc, 346Xg, 372Xd, {\it 383Xf}, 384Q\vfour{, 412Ya, 413Xe, 413Xl, 415Xc, 419I, 419Xf, 439E, 439F, 445Xk, 453Xb, {\it 454Yb}, 481Q, 482Yb\vfive{, - 522A, 528O, 528Za, {\it 533Xa}, 537Za, 547Xe, 553Z, 554Db, + 521Xn, 522A, 528O, 528Za, {\it 533Xa}, 537Za, 547Xe, 553Z, 554Db, 554I, 567Xf, 567Xl}}}}%5%4%3%2 %Lebesgue measure on R @@ -8510,18 +8566,20 @@ 264H, 264I, 266C\vthree{, 342Ja, 344Kb, 345B, 345D, 345Xf\vfour{, 411O, 411Ya, 415Ye, 419Xd, {\it 441Ia}, 441Xg, 442Xf, -{\it 443Ym}, {\it 453B}, 449O, 449Yj, +{\it 443Yq}, {\it 453B}, 449O, 449Yj, 471Yi, 476F-476H, %476F 476G 476H 495Xo\vfive{, 535G, {\bf 565D}, 565E, 565H, 565Xa}}}}%4%5%3%2 % Lebesgue measure on R^r \vtwo{----- ----- (on $[0,1]$, $\coint{0,1}$) 211Q, {\it 216Ab}, -234Ya, 252Yp, 254K, 254Xh, 254Xj-254Xl\vthree{, %254Xj 254Xk 254Xl +234Ya, 252Yp, 254K, 254Xh, 254Xj-254Xl, %254Xj 254Xk 254Xl +254Yh\vthree{, 343Cb, {\it 343J}, 343Xd, 344K, 385Xj, 385Xk, 385Yd\vfour{, - {\it 415Fa}, {\it 417Xi}, {\it 417Xq}, {\it 418Xd}, 419L, {\it 419Xg}, + {\it 415Fa}, 416Yi, {\it 417Xi}, {\it 417Xq}, {\it 418Xd}, +419L, {\it 419Xg}, 433Xf, {\it 435Xl}, {\it 435Xm}, 436Xm, 438Ce, -439Xa, 448Xk, {\it 451Ad}, {\it 454Xa}, +439Xa, 448Xj, {\it 451Ad}, {\it 454Xa}, 457H, 457I, 457Xj-457Xm, %457Xj 457Xk 457Xl 457Xm 457Yd, 457Za, 457Zb, 463Xj, 463Yc, 463Ye, 491Xg, 491Yg, 491Z\vfive{, @@ -8545,7 +8603,7 @@ 374C, 374D, 374Xa, {\it 374Xf}, 374Xh, 374Ya, 374Yd, 375Xe, 375Yd, 394Za\vfour{, 425Zb, 494Xf\vfive{, - 525Q, 525Xc, 532M, 532O, 546Zc}}%4%5 + 525P, 525Xc, 532M, 532O, 546Zc}}%4%5 }%3 % Lebesgue measure @@ -8553,7 +8611,7 @@ 475Ya\vfive{, 565Xb}}%4%5 -\vfive{Lebesgue null ideal 522A, 522M, 522O, 522Va, 522Xc, 522Ya, +\vfive{Lebesgue null ideal 521I, 522A, 522M, 522O, 522Va, 522Xc, 522Ya, 523Ma, 523Ya, 527H, 527J, 527K, 527Xa, 527Ya, 534J, 534Xm, 539Yb, 546Q, 547Xf, 555Yd {\it see also} additivity of Lebesgue measure, @@ -8627,7 +8685,7 @@ \vfour{L\'evy-Ciesielski construction of Wiener measure 477Ya }%4 -\vfour{L\'evy process 455P-455T, %455P 455Q 455R 455S 455T +\vfour{L\'evy process {\bf 455P}, 455Q-455U, %455Q 455R 455S 455T 455U 455Xe, 455Xf, 455Xh-455Xk; %455Xh 455Xi 455Xj 455Xk {\it see also} Brownian motion (\S477) }%4 @@ -8643,7 +8701,7 @@ \indexheader{lexicographic} \vthree{lexicographic ordering {\bf 351Xa}, 352Xf\vfive{, - {\bf 537Cb}, 561Xd}%5 + {\bf 537Cb}, 561Xe}%5 }%3 %Lf%Lg%Lh%Li @@ -8680,6 +8738,12 @@ \vfour{----- on $L^0(\mu)$ 448Q }%4 +\vfour{----- of an action 448S, 448T +}%4 + +\vfour{----- of an additive function 448Yc +}%4 + \vthree{Lifting Theorem 341K, 363Yf\vfour{, 447I\vfive{, 535D, 535H}}%4%5 }%3 @@ -8731,13 +8795,15 @@ ({\bf 467H}) }%4 -\indexheader{linear} -\vthree{linear functional 3A5D\vfour{, {\it 4A4Ac}}; - {\it see also} positive linear functional\vfour{, +\indexiiheader{linear} +\vthree{linear functional 3A5D; + {\it see also}\vfour{ algebraic dual ({\bf 4A4Ac}),} +positive linear functional\vfour{, tight linear functional ({\bf 436Xn})}%4 }%3 -\vthree{linear lifting 341Xf, 341Xg, {\it 345Yb}, {\bf 363Xe}, 363Yf\vfive{, +\vthree{linear lifting 341Xf, 341Xg, {\it 345Yb}, +{\bf 363Xe}, 363Yf\vfive{, {\bf 535O}, 535P-535R, %535P 535Q #535R 535Xi-535Xl, %535Xi 535Xj 535Xk 535Xl 535Yc, 535Ze, {\it 567Xl}; @@ -8748,7 +8814,7 @@ \ifdim\pagewidth>467pt\ifnum\volumeno=3\fontdimen3\tenrm=3.33pt\fi\fi \vtwo{linear operator {\it 262Gc}, 263A, 265B, 265C, {\it \S2A6}\vthree{, 355D, 3A5E\vfour{, - 466Xi, 4A4J\vfive{, + 466Xl, 4A4J\vfive{, 567Hc, 567Xj}}}; %4%3%5 {\it see also} bounded linear operator ({\bf 2A4F})\vthree{, (weakly) compact linear operator ({\bf 3A5L})}, @@ -8779,8 +8845,8 @@ \vtwo{linear topological space 245D, {\it 284Ye}, {\bf 2A5A}, 2A5B, 2A5C, 2A5E-2A5I\vthree{, %2A5Eb 2A5F 2A5G 2A5H 2A5I 367M, 367Yn, 367Yo, 3A4Ad, 3A4Bd, 3A4Fg, 3A5N\vfour{, - 418Xj, 445Yc, 463A, 466Xo, 466Xp, 466Xr, -4A3T, 4A3U, 4A4A, 4A4B, 4A4H\vfive{, + 418Xj, 445Yc, 463A, 466Xm, 466Xn, 466Xo, +4A3T, 4A3U, 4A4A, 4A4B, 4A4Db, 4A4H\vfive{, 537H, 567Hc}; %5 {\it see also} locally convex space ({\bf 4A4Ca})}}%4%3 }%2 @@ -8803,7 +8869,7 @@ 514Nd, 514Xb, 514Ya, 516Lb, 518Cb, 524L, 524Mf, {\it 524Xa}, 528Pa, 528Qb, 528Xg, 539Xa; (of a pre- or partially ordered set) -{\bf 511Be}, 511H, 511Xf, 511Ya, 512Ea, 513Ee, 513Gd, 514Nd, 528Qb, 529Xb; +{\bf 511Bg}, 511H, 511Xh, 511Ya, 512Ea, 513Ee, 513Gd, 514Nd, 528Qb, 529Xb; (of a supported relation) {\bf 512Bc}, 512Dd, 512E, 512Xb, 516J %includes \link_{<\kappa}, \link_{\kappa} }%5 linking number @@ -8823,15 +8889,16 @@ 323Mb\vfour{, 437Yo, 471Xc, 473C-473E, %473C 473D 473Ed 473H-473L, %473H 473I 473J 473K 473L -474B, {\it 474D}, {\it 474E}, {\it 474K}, {\it 474M}, 475K, 475Nb, 475Xg, -475Xm, 476Yb, 479Pc, 479Td, 479U, +474B, {\it 474D}, {\it 474E}, {\it 474K}, {\it 474M}, 475K, 475Nc, 475Xg, +475Xl, 476Yb, 479Pc, 479Td, 479U, 484Xi, 492H, 492Xb-492Xd, %492Xb 492Xc 492Xd {\bf 4A2A}\vfive{, 534Oa}}}; %3%4%5 {\it see also} H\"older continuous ({\bf 282Xj})\vfour{, -Kantorovich-Rubinstein metric ({\bf 437Qb}, {\bf 457Ld}), +Kantorovich-Rubinstein metric ({\bf 437Qb}), lipeomorphism ({\bf 484Q}), -uniformly Lipschitz ({\bf 475Yf})}%4 +uniformly Lipschitz ({\bf 475Ye}), +Wasserstein metric ({\bf 457K})}%4 }%2 Lipschitz fn %Lj%Lk%Lm%Ln%Lo @@ -8865,7 +8932,7 @@ 383Xb, 383Xc, 383Xe, 383Xh, 384M, 384N, 384Pa, 384Ya-384Yd, %384Ya 384Yb 384Yc 384Yd 391Cb, 391Xl, 395Xg, 395Xh, 395Yd, {\it 396A}\vfour{, - 411P, 434T, 494Bd, 494Cf, 494G, 494R, 494Xh\vfive{, + 411P, 434T, 443Xe, 494Bd, 494Cf, 494G, 494R, 494Xh\vfive{, 538Yp, {\it 566K}, 566Oc}}; %4%5 {\it see also} localization ({\bf 322Q}) }%3 localizable measure algebra @@ -8881,7 +8948,7 @@ \vtwo{localizable measure (space) {\bf 211G}, 211L, {\it 211Ya}, 211Yb, 212Ga, 213Hb, 213L-213N, %213L, 213Mb, 213N, -{\it 213Xl}, 213Xm, 214Ie, 214K, 214Xa, 214Xc, 214Xe, 216C, 216E, +213Xm, 214Ie, 214K, 214Xa, 214Xc, 214Xe, 216C, 216E, {\it 216Ya}, 216Yb, 234Nc, 234O, 234Yk-234Yn, %{\it 234Yk} 234Yl 234Ym 234Yn 241G, 241Ya, 243Gb, 243Hb, @@ -8916,7 +8983,7 @@ 437I, 441C, 441H, 441Xn, 441Xs, 452T, 462E, 495Nd, 495O, 4A2G, 4A2Kf, 4A2Qh, 4A2Rk, 4A2Sa, 4A2T\vfive{, - 514A, 514H, 516Q, 516Xc, 516Xh, 517J, 517Pd, 517Xj, 526Ya, 561Xf, 561Yj, + 514A, 514H, 516Q, 516Xc, 516Xh, 517J, 517Pd, 517Xj, 526Ya, 561Xg, 561Ye, 566Xj}%5 }%4 loc cpct Hdorff sp @@ -8929,11 +8996,11 @@ \vfour{locally compact topological group 441E, 441Xh, {\it 441Xq}, 442Ac, 442Xf, 443E, 443K, 443L, 443P-443T, %443P 443Q 443R 443S 443T -443Xq, 443Xr, 443Xt, 443Xv, 443Xw, 443Yc, 443Yf, 443Yp, 443Yr, +443Xq, 443Xr, 443Xt, 443Xv, 443Xw, 443Yc, 443Yh, 443Yr, 443Yt, 445Ac, 445J, 445U, \S446, 447E-447I, %447E 447F 447G 447H 447I -447Xa, 448S, 449H, 449J, 449K, 449Xd, 449Xj-449Xl, %449Xj 449Xk 449Xl -449Xp, 449Yd, 449Yf, 449Yk, -451Yt, 493H, 494Xb, 4A5E, 4A5Jb, +447Xa, 448S, 449H, 449J, 449K, 449Xd, 449Xk-449Xm, %449Xk 449Xl 449Xm +449Xq, 449Yf, +451Yt, 493H, 494Xb, 4A5E, 4A5J, 4A5M-4A5P, %4A5M 4A5N 4A5Oe 4A5P 4A5R, 4A5S\vfive{, 534H, 561G, 564Ya}; %5 @@ -8948,8 +9015,8 @@ }%3 \vfour{locally convex linear topological space - \S461, 462Yb, 463A, 466A, 466K, 466Xa, 466Xc, 466Xd, 466Xj, 466Ya, -466Yc, 466Yd, + \S461, 462Yb, 463A, 466A, 466K, 466Xa, 466Xc, 466Xd, 466Xi, 466Ya, +466Ye, 466Yc, 4A2Ue, 4A3V, {\bf 4A4C}, 4A4E-4A4G\vfive{, %4A4E 4A4F 4A4G 537Hc}%5 @@ -8964,7 +9031,7 @@ \vtwo{locally determined negligible sets {\bf 213I}, 213J-213L, %213J, 213K, 213L, -213Xj-213Xl, %213Xj 213Xk 213Xl +213Xh, 213Xi, 213Xl, 214Ic, 214Xf, 214Xg, {\it 216Yb}, 234Yl, 252E, 252Yb\vfour{, 431Xd\vfive{, 521Xb, {\it 538Na}}%5 @@ -8992,8 +9059,8 @@ %474E 474F 474G 474H 474I 474J 474K 474L 474M 474N 474R, 474S, 474Xa, 474Xd, 474Xe, 475D-475G, %475D 475E 475F 475G -475Jb, 475L-475P, %475L 475Ma 475N 475O 475P -475Xh, 475Ye, 484Ea, 484H-484N, %484Hc 484I 484J 484K 484L 484M 484N +475Jc, 475L-475P, %475L 475Ma 475N 475O 475P +475Xh, 475Yf, 484Ea, 484H-484N, %484Hc 484I 484J 484K 484L 484M 484N 484Rb }%4 locally finite perimeter @@ -9081,7 +9148,7 @@ \vtwo{lower semi-continuous function {\bf 225H}, 225I, 225Xl, 225Xm, 225Yd, 225Ye\vthree{, 323Cb, 367Xx\vfour{, 412W, 412Xr, 412Xs, 414A, 414B, 417B, 437J, -{\it 443Xc}, 444Fa, +443Xc, 444Fa, 452C, 452D, 452Xa, 461C, 461D, 461Kb, 461Xa, 472F, 476B, 478D, 478Ib, 478Jc, 478O, 478P, 478Xc, 478Yi, 478Yj, 479F, 479Jc, 479Xh, {\bf 4A2A}, 4A2Bd, 4A2Gl, 4A3Ce}%4 @@ -9189,8 +9256,8 @@ 331Xi, 331Ye, 331Yh, 331Yj, 332M, 332N, 332R-332T, %332R 332S 332T 333D, 334B, 334D, 334Xb, 369Xg, 375Lb, 387K, 387L, 387Xc, 388K, 388L\vfour{, - 438U, 438Xj, {\it 448Xj}, 494Be, 494Ci, 494E\vfive{, - 521O, 521P, 524M, 524O, 524Pf, + 438U, 438Xj, {\it 448Xi}, 494Be, 494Ci, 494E\vfive{, + 521O, 521P, 524M, 524O, 524Qf, 524Xk, 524Yb, 528H, 528J, 528K, 528N, 528Pa, 528Xg, 529B, 529D, 535I, 535Zd, 531A, 531F, 532B, 533B-533D, %533B 533C 533D @@ -9206,7 +9273,7 @@ 464Qb\vfive{, 521Jb, 521Q-521S, %521Q 521R 521S 521Xh, 521Yb, 521Yd, 524B, 524F-524I, %524F 524G 524H 524I -524R, 524Xf, 524Zb, {\it 527J}, {\it 527Xi}, 536Ce, +524S, 524Xf, 524Zb, {\it 527J}, {\it 527Xi}, 531D, 532A, 536De, 531C, 531Xa, 531Xn, 531Yc, 532Yc, 533Yb, 537Bc, 537S, 543E-543L, %543E 543F 543G 543H 543I 543J 543K 543L 543Xa, 543Xb, 543Ya, 543Z, @@ -9236,7 +9303,7 @@ \vthree{Maharam-type-$\kappa$ component in a Boolean algebra {\bf 332Gb}, 332H, 332J, 332O, 332P, 332Xj, 332Ya, 384N, {\it 395Xh}\vfive{, - 524M, 524P, 524Q, 524T, {\it 525Ha}, 535B, 535Xj}%5 + 524M, 524Q, 524R, 524U, {\it 525Ga}, 535B, 535Xj}%5 }%3 M-type-kappa component %Mai%Maj%Mak%Mal%Mam%Man @@ -9257,7 +9324,7 @@ \vfour{\indexheader{marginal} marginal measure 437Xn, {\bf 452L}, {\it 452M}, 454T, -457L, 457Xo, 457Xr\vfive{, +457Lb, 457Xo, 457Xr\vfive{, 531C, 535Xl, 533Xf}%5 }%4 @@ -9268,8 +9335,7 @@ \indexiiheader{Markov} \vfour{Markov process 455A-455E, %455A 455B 455C 455D 455E 455G-455K, %455G 455H 455I 455J 455K -455O, 455S, -455Xa-455Xd, %455Xa 455Xc 455Xb 455Xd +455O, 455Xa-455Xd, %455Xa 455Xc 455Xb 455Xd 455Xf, 455Yb, 455Yd; {\it see also} L\'evy process, Brownian motion }%4 @@ -9298,7 +9364,7 @@ }%5 \vfive{Martin number (of a pre- or partially ordered set) -{\bf 511Bh}, 511Dg, 511Xf, +{\bf 511Bh}, 511Dg, 511Xh, 517A-517H, %517A 517B 517C 517D 517E 517F 517G 517H 517O-517Q, %517O 517Pc 517Q 517Xa, 517Xb, 517Xd-517Xf, %517Xd 517Xe 517Xf @@ -9325,8 +9391,8 @@ 367J, 367Q, 367Yt, 369Xq}%3 }%2 -\vtwo{martingale difference sequence {\bf 276A}, 276B, 276C, 276E, 276Xd, -276Xg, 276Ya, 276Yb, 276Ye, 276Yg +\vtwo{martingale difference sequence {\bf 276A}, 276B, 276C, 276E, 276Xe, +276Xf, 276Ya, 276Yb, 276Ye, 276Yg }%2 \vtwo{martingale inequalities 275D, 275F, 275Xb, @@ -9421,7 +9487,7 @@ \vthree{measurable algebra {\bf 391B}, 391C, 391D, 391K, 391Xf, 391Xl, 392G, 393D, 393Eb, 393Xg, 393Xj, {\it 394Nc}, 395P, 395Q, 395Xf, 396B\vfive{, - 515Xe, 524Nb, 524Xj, 524Yb, 525Fb, 525J, 525L, 525M, 525Pb, 525Ub, 525Xb, + 515Xe, 524Nb, 524Xj, 524Yb, 525Eb, 525I, 525K, 525L, 525Ob, 525Tb, 525Xb, 529D, 535Ea, 533J, 539N-539P, %539N 539Ob 539Pf 539Yb, 545G, 546M, 546Yb, 546Zb, 556P, 561Yi, 566Mb, 566Nc, 566Xf, 566Z}; %5 @@ -9434,8 +9500,7 @@ measurable cover {\it see} measurable envelope ({\bf 132D}) measurable envelope {\bf 132D}, 132E, 132F, 132Xg, 134Fc, 134Xd\vtwo{, - 213K-213M, %213K 213L 213M -214G, 216Yc, 266Xa\vthree{, + 213L, 213M, 214G, 216Yc, 266Xa\vthree{, 322I, 331Xl\vfour{, 413Ei, 419I, {\it 414Xl}, {\it 414Xo}, {\it 414Xp}\vfive{, 535Xa}}}}; %2%3%4%5 @@ -9450,7 +9515,7 @@ measurable function (taking values in $\Bbb R$) \S121 ({\bf 121C}), 122Ya\vtwo{, - 212B, 212Fa, 213Yd, 214Ma, 214Na, 235C, 235I, 252O, 252P, 256F, 256Yb, + 212B, 212Fa, 213Ye, 214Ma, 214Na, 235C, 235I, 252O, 252P, 256F, 256Yb, 256Yc\vthree{, 316Yi, 322Yf\vfour{, 413G, 414Xf, 414Xk, 414Xr, 418Xl, 418Xm, 418Xq, 463M, 463N, 482E, @@ -9480,7 +9545,7 @@ ----- ----- ($(\Sigma,\Tau)$-measurable function) {\bf 121Yc}\vtwo{, 235Xc, 251Ya, 251Yd\vthree{, 343A, 364Q\vfour{, - 411L, 411Yp, 423O, 424B, 424Xh, 434De, 443Yh, {\it 443Yi}, 448S, 451Ym, + 411L, 423O, 424B, 424Xh, 434De, 441Yp, 443Yi, {\it 443Yj}, 448S, 451Ym, 455Ld, {\bf 4A3B}, 4A3C, 4A3Db, 4A3K, 4A3Ne\vfive{, {\it 527F}, 551C-551E, %551C 551D 551Ea 551M, 551N}%5 @@ -9530,8 +9595,8 @@ \vtwo{\indexheader{measure algebra}} \vtwo{measure algebra 211Yb, 211Yc\vthree{, vol.\ 3 ({\bf 321A})\vfour{, - 435Xm, 448Xj, 493H, 495J, 495Xg\vfive{, - 515Xe, 524M, 525E, 563M, 563N, 566L}}; + 435Xm, 448Xi, 493D, 493Ya, 495J, 495Xg\vfive{, + 515Xe, 524M, 525D, 563M, 563N, 566L}}; isomorphic measure algebras 331I, 331L, 332B, 332C, 332J, 332K, 332P, 332Q, 332Ya, 332Yb }%3 @@ -9541,9 +9606,9 @@ 321H-321K ({\bf 321I}), %321H 321I 321J 321K 322B, 322O, {\it 327C}\vfour{, 412N, 414A, 415L, {\it 416C}, {\it 416Wb}, 418T, 441Ka, 441Yl, 441Yn, -448Xk, 458Lb, 474 {\it notes}\vfive{, - 521B, 521J, 524J, 524K, -524P, 524Q, 524S, 524T, 525B-525D, %525B 525C 525D +443Xe, 448Xj, 458Lb, 474 {\it notes}\vfive{, + 521B, 521J, 524J, 524K, 524P-524R, %524P 524Q 524R +524T, 524U, 525B, 525C, 525Xa, 525Xd, 527O, 527Ye, 531A, 531B, 531F, 533A, 538Ja, 538K, 543J, 563M, 563N, 565Ya, 566Lb}}; %5%4 {\it see also }\vfour{Haar measure algebra ({\bf 442H}),} @@ -9556,7 +9621,7 @@ {\it 324Kb}, 324Xb, {\it 324Xc}, 327B, 327C, 331O, 331Yj, 365Ea, 367R, 367Xs, 367Yp, 393Xi\vfour{, - 411Yc, 412N, 443Aa, 443C, 444Fc, 444Yd, 448S, 448T, 448Xj, + 411Yc, 412N, 443Aa, 443C, 444Fc, 444Yd, 448S, 448T, 448Xi, 493D, 494Bb, 494Xc, 494Xh, 498A\vfive{, 521Oa, 528E, 531Ja, 538Yp, 563M}}; %4%5 {\it see also} strong measure-algebra topology ({\bf 323Ad}) @@ -9605,24 +9670,24 @@ }%5 \vfour{measure-free weight 438D-438H, %438D, 438E, 438F, 438G 438H, -438J, 438M, 438U, 438Xh, 438Xi, 438Xk, 438Xm, 438Yl, 448Xi, 467Pb +438J, 438M, 438U, 438Xh, 438Xi, 438Xk, 438Xm, 438Yl, 448Xh, 467Pb }%4 \vthree{\indexheader{measure metric}} \vthree{measure metric (on a measure algebra) {\bf 323A}, 323M, {\it 323Xb}, 324Yg\vfour{, - 448Xk, 493G, 494Xa, 494Xl}%4 + 448Xj, 494Xa, 494Xl}%4 }%3 \vfive{\indexheader{measure-precaliber}} -\vfive{measure-precaliber {\bf 511Ed}, 525F-525H, %525F 525G 525Hb -525K, 525N, 525Pa, 525Ud, 525Xf, 525Z, 531M, 531P, 544D +\vfive{measure-precaliber {\bf 511Ed}, 525E-525G, %525E 525F 525Gb +525J, 525M, 525Oa, 525Td, 525Xh, 525Z, 531M, 531P, 544D }%5 -\vfive{measure-precaliber pair {\bf 511Ed}, 525Xg, 525Xh, 531Lb, 531O +\vfive{measure-precaliber pair {\bf 511Ed}, 525Xf, 525Xg, 531Lb, 531O }%5 -\vfive{measure-precaliber triple {\bf 511Ed}, 525E, 525Ha, 525J, 525Ua +\vfive{measure-precaliber triple {\bf 511Ed}, 525D, 525Ga, 525I, 525Ta }%5 \indexiiiheader{measure-preserving} @@ -9638,7 +9703,7 @@ 388J-388L, %388J 388K 388L 388Xa-388Xc, %388Xa 388Xb 388Xc 388Yd\vfour{, - 443Yu\vfive{, + 443Yf\vfive{, 556Kd, 556N}}; %4%5 {\it see also} automorphism group of a measure algebra, two-sided Bernoulli shift ({\bf 385Qb}) @@ -9725,7 +9790,7 @@ }%4 \indexheader{metric} -\vtwo{metric {\bf 2A3F}, 2A4Fb\vfour{, 4A2Ji}; +\vtwo{metric {\bf 2A3F}, 2A4Fb\vfour{, 4A2Jb}; \vthree{{\it see also} entropy metric ({\bf 385Xq}),} Euclidean metric ({\bf 2A3Fb})\vfour{, Hamming metric ({\bf 492D})}, @@ -9736,7 +9801,8 @@ pseudometric {\bf 2A3F})\vfour{, product metric, right-translation-invariant metric ({\bf 4A5Q}), - total variation metric ({\bf 437Qa})} + total variation metric ({\bf 437Qa}), + Wasserstein metric ({\bf 457K})}%4 }%2 \vfour{metric gauge {\it see} uniform metric gauge ({\bf 481Eb}) @@ -9748,7 +9814,7 @@ \vtwo{metric space {\it 224Ye}, {\it 261Yi}\vthree{, 316Yk, 3A4F, 3A4Hc\vfour{, - 434L, 437Rg, 437Yo, 437Yp, 448Xi, 457K, 457L, 457Xq, + 434L, 437Rg, 437Yo, 437Yp, 448Xh, 457K, 457L, 457Xq, {\it \S471}, 482E, {\it 484Q}, 4A2Lg\vfive{, 546N, 565N, 565O, 566Xa}}}; %3%4%5 {\it see also} complete metric space\vfour{, @@ -9777,8 +9843,8 @@ 451R-451T, %451R 451S 451T 451Xo, 462Xa, {\it 491Cg}, 491Xj, 496Yb, 4A2L, 4A2Nh, 4A2Qh, 4A3Kb, 4A4Cf, {\it 4A5Jb}\vfive{, - 535K, 535N, 533Ca, 533D, 533G, 544K, 544L, 544Ya, 561Yf, -5A4Bh, 5A4H}}}; %3%4%5 + 535K, 535N, 533Ca, 533D, 533G, 544K, 544L, 544Ya, 561Xk, 561Yf, +5A4Bh}}}; %3%4%5 {\it see also}\vfour{ compact metrizable,} metric space\vfive{, metrizably compactly based ({\bf 513K})}, separable metrizable\vfour{, @@ -9791,7 +9857,7 @@ {\it see also} normed space }%3 -\vfour{----- topological group 443Yn, 444Ye, 446Ec, 494Ch, 494Xg, +\vfour{----- topological group 443Yo, 444Ye, 446Gc, 494Ch, 494Xg, 4A5Q, 4A5R\vfive{, 567H};%5 {\it see also} Polish group ({\bf 4A5Db}) @@ -9858,17 +9924,16 @@ \indexheader{modular} \vfour{modular function (of a group carrying Haar measures) {\bf 442I}, 442J, 442K, 442Xf, 442Xh, 443G, 443R-443T, %443R 443S 443T -443Xn, 443Ys, {\it 444J}, 444Mb, 444O, 444Xy, {\it 447E}, {\it 447F}, -{\it 449Yd} +443Xn, 443Yu, {\it 444J}, 444Mb, 444O, 444Xy, {\it 447E}, {\it 447F} }%4 \vfour{modular functional on a lattice 361Xa, {\bf 413Xq}, 435Xn\vfive{, 563D, 563H, 563L, 565Cc}; %5 - {\it see also} supermodular ({\bf 413P}) -}%4 432aA, 432aC + {\it see also} submodular ({\bf 432Jc}), supermodular ({\bf 413P}) +}%4 \indexheader{modulation} -\vtwo{modulation \S284 {\it notes}, {\bf 286C} +\vtwo{modulation 284Xd, \S284 {\it notes}, {\bf 286C} }%2 \indexheader{monocompact} @@ -9894,7 +9959,7 @@ (space of monotonic functions) {\it 463Xg}, {\it 463Xh} }}}%4%3%2 -%monotonically normal 4A2Rc 561Xp +%monotonically normal 4A2Rc 561Xl \indexiiheader{Monte} \vtwo{Monte Carlo integration 273J, 273Ya\vfour{, 465H, 465M}%4 @@ -10032,7 +10097,8 @@ \indexheader{network} \vfour{network in a topological space 438Ld, 466D, 467Pb, 467Ye, -{\bf 4A2A}, 4A2Ba; +{\bf 4A2A}, 4A2Ba\vfive{, + 561Ye}; %5 {\it see also} countable network }%4 @@ -10077,7 +10143,7 @@ \indexheader{no} \vfour{no small subgroups (in `topological group with no small subgroups') -{\bf 446E}, 446H-446K, %446H 446I 446J 446K +{\bf 446G}, 446H-446K, %446H 446I 446J 446K 446M, 446O }%4 @@ -10122,7 +10188,7 @@ }%2 \indexheader{normal} -\vtwo{normal density function 274A, 283N, 283We, 283Wf\vfour{, 456Aa} +\vtwo{normal density function 274A, 283N, 283Wi, 283Wj\vfour{, 456Aa} }%2 \vtwo{normal distribution {\bf 274Ad}, 495Xh; @@ -10165,7 +10231,7 @@ \vfour{----- ----- of a topological group 443S, 443T, 443Xt-443Xw, %443Xt 443Xu 443Xv 443Xw -{\it 443Yf}, 443Yn, {\it 449C}, {\it 449Fb}, {\it 493Bc}, +{\it 443Yh}, 443Yo, {\it 449C}, {\it 449Fb}, {\it 493Bc}, 4A5J-4A5L, %4A5Jb 4A5K 4A5L 4A5S }%4 @@ -10178,7 +10244,7 @@ 438Jb, 438Yf, 438Yj, {\it 491Cd}, 491Xq, {\bf $\pmb{>}$4A2A}, 4A2F-4A2H, %4A2F 4A2Gb 4A2Hb 4A2Rc, 4A3Yc\vfive{, - 531L, 531T, 531Xg, 561Xf, {\it 561Xp}, 5A4Fa}; %5 + 531L, 531T, 531Xg, 561Xg, {\it 561Xl}, 5A4Fa}; %5 {\it see also} %monotonically normal {(\bf 4A2A}), perfectly normal ({\bf 4A2A}) }%4 @@ -10198,7 +10264,8 @@ \vfour{normalized Hamming metric {\bf 492D} }%4 -\vtwo{normalized Hausdorff measure 264 {\it notes}, \S265 ({\bf 265A})\vfour{, +\vtwo{normalized Hausdorff measure 264 {\it notes}, +\S265 ({\bf 265A})\vfour{, chap.\ 47}%4 }%2 @@ -10216,7 +10283,7 @@ \vtwo{normed space {\it 224Yf}, \S2A4 ({\bf 2A4Ba})\vthree{, 394Q\vfour{, {\it 451Xr}, {\it 461G}, 462D, 466C-466E, %466C 466D 466E -466Ye, \S467, 4A4I\vfive{, +466H, 466Yb, \S467, 4A4I\vfive{, {\it 567Xj}}}}; %3%4%5 {\it see also} Banach space ({\bf 2A4D}) }%2 @@ -10273,7 +10340,7 @@ 412Xc, 413Xi\vfive{, 521A, 521C-521J, %521C 521D 521E 521F 521G 521H 521I 521J \S523, 524B, 524F-524K, %524F 524G 524H 524I 524J 524K -524P, 524R-524T, %524R, 524Sb, 524T, +524Q, 524S-524U, %524S, 524Tb, 524U, 524Xi, {\it 527Bc}, 527C, 527G, 527J, 527Xi, 534B, 534Yb, {\it 543Ab}, 544E, 544F, 544Xc, 546N, {\it 546O}, 547I, {\it 551Xb}, 555C, 563Ab, 563Fc; @@ -10291,7 +10358,7 @@ \indexmedskip%Oa%Ob%Oc%Od \indexheader{odd} -\vtwo{odd function 255Xb, 283Yd +\vtwo{odd function 255Xb, 283Ye }%2 \vthree{\indexheader{odometer}} @@ -10312,7 +10379,7 @@ %Om%On \vfour{\indexheader{one-parameter}} -\vfour{one-parameter subgroup (in a topological group) 446I +\vfour{one-parameter subgroup (in a topological group) {\it 446 notes} }%4 \vthree{\indexheader{one-point}} @@ -10455,7 +10522,7 @@ \vthree{order-continuous order-preserving function {\bf 313Ha}, 313I, 313Xi, 313Yb-313Yd, %313Yb, {\it 313Yc}, 313Yd, 315D, {\it 315Yg}, 316Fc, {\it 326Oc}, 361Cf, -361Gb, 363Eb, 363Ff, 367Xb, 367Yc, 385Ya, 386Yb, 386Yc, +361Gb, 361Xl, 363Eb, 363Ff, 367Xb, 367Yc, 385Ya, 386Yb, 386Yc, 392Xb, 393C, {\it 393Xa}, 393Xc, 395N\vfour{, 4A2Ro}; %order-continuous order-preserving function @@ -10597,7 +10664,7 @@ \indexiiheader{ordinal} \vtwo{ordinal {\bf 2A1C}, 2A1D-2A1F, %2A1D, 2A1E, 2A1F, 2A1K\vfive{, - 518Xb, 561A, 5A3N}%5 + 518Xb, 561A, 5A3Na}%5 }%2 \vfive{ordinal function of Boolean algebras 514G; @@ -10678,7 +10745,7 @@ \indexheader{outer measure} outer measure \S113 ({\bf 113A}), 114Xd, {\bf 132B}, {\it 132Xg}, 136Ya\vtwo{, - {\it 212Xf}, 213C, 213Xa, 213Xg, 213Xk, 213Ya, 251B, 251Wa, {\it 251Xe}, + {\it 212Xf}, 213Xa, 213Xg, 213Xi, 213Yb, 251B, 251Wa, {\it 251Xe}, 254B, {\it 264B}, {\it 264Xa}, {\it 264Ya}, {\it 264Yo}\vfour{, 413Xd, 452Xi}}; %2%4 {\it see also} Lebesgue outer measure ({\bf 114C}, {\bf 115C})\vtwo{, @@ -10690,14 +10757,14 @@ 132Xa-132Xi, %132Xa 132Xb 132Xc 132Xd 132Xe 132Xf 132Xg 132Xh 132Xi 132Xk, 132Ya-132Yc, %132Ya 132Yb 132Yc 133Je\vtwo{, - 212Ea, {\it 212Xa}, 212Xb, 213C, 213F, 213Xa, 213Xg-213Xj, %213Xg, 213Xh, 213Xi 213Xj -213Xk, 213Yd, 214Cd, {\it 215Yc}, 234Bf, 234Ya, + 212Ea, {\it 212Xa}, 212Xb, 213C, 213Fb, 213Xa, 213Xg, 213Xi, 213Xj, +213Yb, 213Ye, 214Cd, {\it 215Yc}, 234Bf, 234Ya, 251P, 251S, 251Wk, 251Wm, 251Xn, 251Xq, {\it 252D}, {\it 252I}, {\it 252O}, 252Ym, {\it 254G}, 254L, 254S, 254Xb, 254Xq, 254Yd, 264Fb, 264Ye\vfour{, 412Ib, 412Jc, 413E-413G, %413E 413F 413G 413Xd, 417Xj, 431E, 431Xd, 432Xf, 451Pc, 451Xm, -457Xg, {\it 463I}, {\it 463Xa}, {\it 464C}, {\it 464D}, 471Dc, +457Xi, {\it 463I}, {\it 463Xa}, {\it 464C}, {\it 464D}, 471Dc, 471Yb\vfive{, 543D, 552D, 552Ya}}%5%4 }%2 @@ -10770,7 +10837,7 @@ \indexheader{partially} \vtwo{partially ordered linear space {\bf 241E}, 241Yg\vthree{, - 326C, \S351 ({\bf 351A}), 355Xa, 361C, 361G, 362Aa; + 326C, \S351 ({\bf 351A}), 355Xa, 361C, 361G, 361Xl, 362Aa; {\it see also} Riesz space ({\bf 352A}) }%3 }%2 @@ -10779,8 +10846,8 @@ 313D, 313Fa, 313H, 313I, 313Xb, 313Xc, 313Xg, 313Xh, 313Yb, 315C, 315D, 315Xd, {\it 315Yg}\vfour{, 461Ka, {\it 466G}\vfive{, - 511A, 511Bj, 511H, 511Xa, 511Xf-511Xh, %511Xf 511Xg 511Xh -511Xj, 511Xk, 511Ya, 512Ea, 512He, 512K, \S513, + 511A, 511H, 511Xa, 511Xh-511Xj, %511Xh 511Xi 511Xj +511Xl, 511Xm, 511Ya, 512Ea, 512He, 512K, \S513, 514Ng, 514U, 514Xg; {\it see also} pre-ordered set ({\bf 511A})}%5 }%4 @@ -10808,7 +10875,8 @@ %Pb%Pc%Pd%Pe \indexheader{Peano} -Peano curve 134Yl-134Yo %134Yl 134Ym 134Yn 134Yo +Peano curve 134Yl-134Yo\vtwo{; %134Yl 134Ym 134Yn 134Yo + {\it see also} space-filling curve}%2 \indexheader{perfect} \vthree{perfect measure (space) {\bf 342K}, 342L, 342M, @@ -10821,7 +10889,7 @@ 451M-451P, %451M 451N 451O 451P 451Xa, 451Xc, 451Xe, 451Xg, 451Xk, 451Xn, 451Yk, 454Ab, 454C-454E, %454C 454D 454E -454G, 457F, 463I-463L, %463I 463J 463K 463L +454G, 457F, 463I-463M, %463I 463J 463K 463L 463M 498Ya, 495F, 495Xf\vfive{, 521I, 522Va, 527G, 535Yd, 536Xb, 536Ya, 538G-538K, %538G 538I 538J 538K @@ -10854,8 +10922,8 @@ }%4 perf norm top sp \indexheader{perimeter} -\vfour{perimeter {\bf 474D}, 474T, 475M, 475Q, -475Xj-475Xm, %475Xj 475Xk {\it 475Xl} 475Xm +\vfour{perimeter {\bf 474D}, 474T, 475M, 475Q, 475S, 475T, +475Xj-475Xm, %475Xj 475Xk {\it 475Xm} 475Xl 484B-484D, %484B 484C {\it 484D} 484F, 484Ya, 484Yb; {\it see also} Cauchy's Perimeter Theorem (475S), finite perimeter, @@ -10870,7 +10938,7 @@ \indexheader{periodic} \vthree{periodic Boolean automorphism {\bf 381Ac}, 381H, 381R, 381Xe, 381Xg, 381Xo, 382Fb\vfour{, - 494Cc, 494Yf}%4 + 494Cc}%4 }%3 \vtwo{periodic extension of a function on $\ocint{-\pi,\pi}$ {\bf 282Ae} @@ -10976,18 +11044,18 @@ 463Ya, 463Yc-463Ye, %463Yc, 463Yd, 463Ye, 463Za, 463Zb, 464E, 464Yb, 465Db, 465Nd, {\it 465V}, 465Xg, 465Xl, 465Xo\vfive{, - \S536}; %5 %536A 536B 536C 536Xa, 536Xb, 536Ya + \S536}; %5 %536A 536B 536C 536D 536Xa, 536Xb, 536Ya {\it see also} Eberlein compactum ({\bf 467O}) }%4 ptwise cpct set \vtwo{pointwise convergence (topology on a space of functions) 281Yf\vfour{, - 437Xi, 438Q, 438S, 438Xs, 438Yh, 443Yr, 454Sa, {\bf 462Ab}, 462C, + 437Xi, 438Q, 438S, 438Xs, 438Yh, 443Yt, 454Sa, {\bf 462Ab}, 462C, 462E-462J, %462E 462F 462G 462H 462I 462J 462L, 462Xd, 462Ya, 462Yd, 462Ye, 462Z, \S463, 464E, 464Yb, 465Cb, 465G, 465Xk, -465Xl, 465Yi, 466Xn, 466Yc, 467Pa, 467Ye, -476Yb, 494Xa, 494Xl, 4A2Nj, 4A3W\vfive{, +465Xl, 465Yi, 466Xg, 467Pa, 467Ye, +476Yb, 4A2Nj, 4A3W\vfive{, \S536}; %5 {\it see also} pointwise compact}%4 }%2 @@ -10995,8 +11063,9 @@ \vfour{---- (on an isometry group) 441G, 441Xn-441Xr, %441Xn 441Xo 441Xp 441Xq 441Xr -441Yh, 441Yk, 443Xw, 443Yq, 446Yc, 448Xk, 449Xc, 449Xg, 476Xd, -493G, 493G, 493Xb, 493Xd, 493Xe, 494Xa, 494Xl, 497Xb +441Yh, 441Yk, 443Xw, 443Ys, 446Yc, 448Xj, 449Xc, 449Xh, 476Xd, +493G, 493Xb, 493Xd-493Xf, %493Xd, 493Xe, 493Xf, +494Xa, 494Xl, 497Xb }%4 %pointwise convergence @@ -11009,8 +11078,8 @@ }%2 \vtwo{\indexheader{Poisson}} -\vtwo{Poisson distribution 285Q, 285Xo\vfour{, 455Xh, 495A, 495B, 495D, -{\it 495M}, 495Xg; +\vtwo{Poisson distribution 285Q, {\bf 285Xo}\vfour{, + 455Xh, {\bf 495A}, 495B, 495D, {\it 495M}, 495Xg; {\it see also} compound Poisson distribution}%4 }%2 @@ -11028,9 +11097,7 @@ \vtwo{Poisson's theorem 285Q }%2 -\vfour{\indexheader{Pol}} -\vfour{Pol, R.\ 463 {\it notes} -}%4 +%\vfour{\indexheader{Pol}} \vtwo{\indexheader{polar}} \vtwo{polar coordinates 263G, 263Xf @@ -11043,9 +11110,9 @@ }%4 \vfour{\indexheader{Polish}} -\vfour{Polish group 424H, 441Xp, 441Xq, 441Yi, 448P, 448S, 448Xg, 448Xj, -448Xk, {\it 449G}, 449K, 449Xd, -455R, 493Xe, 494Be, 494Ci, 494Yb, {\bf 4A5Db}, {\it 4A5Q}, 4A5S\vfive{, +\vfour{Polish group 424H, 441Xp, 441Xq, 441Yi, 448P, 448S, 448Xf, 448Xi, +448Xj, 449G, 449Xd, +455R, 493Xf, 494Be, 494Ci, 494Yb, {\bf 4A5Db}, {\it 4A5Q}, 4A5S\vfive{, 567Ha}%5 }%4 @@ -11053,11 +11120,11 @@ 418C, 423Ba, 423I, 423Xa, 423R, 424F, 424H, 424Ya, 424Yb, 425Bb, 433Xf, 433Yc, 437Rh, 437Vg, 438P, 438Q, 438S, -441Xp, 448R, 448T, 452Xt, 454B, {\it 454R}, 454Xl, 454Xm, 455M, +441Xp, 448Ra, 448T, 452Xt, 454B, {\it 454R}, 454Xl, 454Xm, 455M, {\bf 4A2A}, 4A2Q, 4A2U, 4A3H, 4A3I, 4A3W, 4A5Jb\vfive{, 513Yf, 517Pd, {\it 522Vb}, 526Hd, 526Xe, 526Xf, -529Ya, 546J, 561Yd, 562E, 562Yb, 562Yc, 563Ff, 564O, 567Xg, -5A4I, 5A4J}; %5 +529Ya, 546J, 562F, 562Ya, 562Yc, 562Yd, 563Ff, 564O, 567Xg, +5A4H, 5A4I}; %5 {\it see also} standard Borel space ({\bf 424A}) }%4 Polish topological space @@ -11085,7 +11152,7 @@ \vtwo{positive cone 253Gb, 253Xi, 253Yd\vthree{, {\bf 351C}}%3 }%2 -\vtwo{positive definite function 283Xt, 285Xr\vfour{, +\vtwo{positive definite function 283Xs, 285Xr\vfour{, {\bf 445L}, 445M, 445N, 445P, 445Xe-445Xh, %445Xe 445Xf 445Xg 445Xh 445Xo, 456Xc, 461Xk}%4 @@ -11131,7 +11198,7 @@ \vfour{----- (usual topology of) 423Ye, 463A, 463I, 463J, {\bf 4A2A}, 4A2Ud\vfive{, - 538Sb, 561Xr, 567Xr}%5 + 538Sb, 561Xd, 567Xr}%5 }%4 \ifnum\volumeno=1{power set $\Cal P\Bbb N$ }\else{----- $\Cal P\Bbb N$ }\fi @@ -11165,10 +11232,10 @@ \vfive{\indexheader{precaliber} precaliber (of a Boolean algebra) {\bf 511Ec}, 516Lc, 516Rb, 516Xb, 517Lb, 517Xf, 528Xe, 541Cc; - (of a measure algebra) 525Dc, 525F, 525H, 525L, 525M, 525O, 525Pb, + (of a measure algebra) 525Cc, 525E, 525G, 525K, 525L, 525N, 525Ob, 525Xb, 525Xc, 553F, 552Xd; (of a pre- or partially ordered set) -{\bf 511Ea}, 511Xg, 511Xh, 516Kc, 516Xb, 517Fb, 517Hb, 517O, 517Xk; +{\bf 511Ea}, 511Xi, 511Xj, 516Kc, 516Xb, 517Fb, 517Hb, 517O, 517Xk; (of a supported relation) {\bf 516A}, 516B-516E; %516Bb, 516C, 516D, 516E; (of a topological space) {\bf 511Eb}, 516Nc, 516Qb, 516Xh; @@ -11178,21 +11245,21 @@ \vfive{precaliber pair (of a Boolean algebra) {\bf 511Ec}, 516L, 516Ra, 516Sa, 517Ig; - (of a measure algebra) 525Da, 525Jb, 525Q, 525Xa, 525Xd, 525Xe, 554Dc; + (of a measure algebra) 525Ca, 525Ib, 525P, 525Xa, 525Xd, 525Xe, 554Dc; (of a pre- or partially ordered set) -{\bf 511Ea}, 516K, 517Fa, 517Hb, 525Xa; +{\bf 511Ea}, 516K, 516Xm, 517Fa, 517Hb, 525Xa; (of a supported relation) {\bf 516A}, 516B-516E, %516B 516C 516D 516E 525Xd; - (of a topological space) {\bf 511Eb}, 511Xl, 516N, 516Qa + (of a topological space) {\bf 511Eb}, 511Xb, 516N, 516Qa }%5 \vfive{precaliber triple (of a Boolean algebra) {\bf 511E}, 511Xa, 516Fb, 516H, 516L, 516M, 516Xc, 516Xd, 516Xf, 516Xk, 539Jc; - (of a measure algebra) 525C, 525E, 525J, 525Ub; + (of a measure algebra) 525B, 525D, 525Ia, 525Tb; (of a pre- or partially ordered set) -{\bf 511E}, 516Fa, 516G, 516K, 516P, 516T, 516Xd, 525C; +{\bf 511E}, 516Fa, 516G, 516K, 516P, 516T, 516Xd, 525B; (of a supported relation) {\bf 516A}, 516B-516F, %516B 516C 516D 516E 516F 516J, 516M, 516Xc; @@ -11217,7 +11284,7 @@ \indexheader{pre-Radon} \vfour{pre-Radon (topological) space {\bf 434Gc}, 434J, 434Ka, 434Xn, {\it 434Xo}, 434Xt, 434Ye, 434Yq, -435Xk, {\it 439Xm}, 462Z, 466B, {\it 466Xf}; +435Xk, {\it 439Xm}, 462Z, 466B; {\it see also} Radon space ({\bf 434C}) }%4 @@ -11270,7 +11337,7 @@ 386L-386O, %386L 386M 386N 386O 386Xe, 386Yb, 386Yc, {\it \S387}, 391B\vfour{, 491Ke, 491P\vfive{, - 546L, 556K, 556L, 556N, 556Q}}%4%5 + 546L, 556K, 556L, 556N, 556Q, 561Yc}}%4%5 }%3 prob alg \vthree{probability algebra free product 325F, 325G, @@ -11323,7 +11390,7 @@ %product group (see product topological group) -\vfour{product linear topological space 466Xp, 467Xc, 4A4B +\vfour{product linear topological space 466Xn, 467Xc, 4A4B }%4 \vtwo{product measure chap.\ 25\vfour{, @@ -11360,12 +11427,12 @@ \vtwo{product probability measure \S254 ({\bf 254C}), 272G, 272J, 272M, 273J, 273Xj, 275J, 275Yj, 275Yk, {\it 281Yk}\vthree{, 325I, 334C, 334E, 334Xd, 334Xe, 334Ya, 342Gf, 342Xn, 343H, \S346, 372Xf, {\it 385S}\vfour{, - 412T-412V %412T 412U 412V + 411Xk, 412T-412V %412T 412U 412V 413Yb, 415E, 415F, 415Xj, 416U, 417E, 417Xs, 417Xv, 417Yf, 417Yg, 433I, 443Xp, 451J, 451Yp, 453I, 453J, 454Xj, 456Aa, 456B, 456Xb, 457K, 458Xo, 465H-465M, %465H 465I 465J 465K 465L 465M -466Xp, 491Eb, 491Xs, 498Xc, 498Ya, 495P, 495Xc, 495Xj, 495Xo\vfive{, +466Xn, 491Eb, 491Xs, 498Xc, 498Ya, 495P, 495Xc, 495Xj, 495Xo\vfive{, 521H, 521Xd, 524Yc, 532E, 532F, 532Xf, 555F, 564O, 564Xd, {\it 566C}, 566I, 566J, 566U}}}; %3%4%5 {\it see also }\vfour{quasi-Radon product measure ({\bf 417R}), @@ -11398,12 +11465,13 @@ % product \vtwo{product topology 281Yc, {\bf 2A3T}\vthree{, - 315Xh, 315Yb, {\it 315Yd}, {\it 323L}, 391Yc, {\bf 3A3I}, 3A3J, 3A3K\vfour{, + 315Xh, 315Yb, {\it 315Yd}, {\it 323L}, 391Yc, +{\bf 3A3I}, 3A3J, 3A3K\vfour{, 417Xt, 418B, 418Dd, 418Xb, 418Xd, 418Yb, 419Xg, {\it 422Dd}, 422Ge, 423Bc, 434Jh, 434Pb, 434Xc, 434Xe, 434Xk, 434Xs-434Xu, %434Xs 434Xt 434Xu 435Xk, 436Xg, 437Vd, 437Yy, {\it 438E}, 438Xp, 438Xq, 439Xg, {\it 439Yh}, -{\it 454T}, {\it 463M}, 467Xa, +{\it 454T}, 467Xa, 4A2B-4A2F, %4A2B 4A2Cb 4A2Da 4A2E 4A2Fh 4A2L-4A2R, %4A2L 4A2Mb 4A2Ne 4A2Od 4A2Pa 4A2Qc 4A2Rl 4A3C-4A3E, %4A3Cf, 4A3Dc, 4A3E, @@ -11572,8 +11640,9 @@ \indexheader{quasi-homogeneous} \vthree{quasi-homogeneous measure algebra {\bf 374G}, 374H-374M, %374H 374I 374J 374K 374L 374M -374Xl, 374Ye, 395Xg\vfive{, - 528Db, 528Fc, 528Xb, 528Ya}%5 +374Xl, 374Ye, 395Xg\vfour{, + 443Xe\vfive{, + 528Db, 528Fc, 528Xb, 528Ya}}%4%5 }%3 \indexvheader{quasi-measurable} @@ -11588,7 +11657,7 @@ }%3 \vtwo{\indexheader{quasi-Radon}} -\vtwo{quasi-Radon measure (space) 256Ya, 263Ya\vfour{, +\vtwo{quasi-Radon measure (space) 256Ya, {\it 263Ya}\vfour{, {\bf 411Ha}, 411Pd, 411Yc, 414Xj, \S415, 416A, 416C, 416G, 416Ra, 416T, 416Xv, 418Hb, 418K, 418Xi, 418Xn, 432E, {\it 434A}, 434H-434J, %434Ha 434Ib 434J, @@ -11605,8 +11674,8 @@ 456Aa, 456P, 456Q, 456Xg, 459G, 466A, 466B, 466K, 466Xa-466Xd, %466Xa 466Xb 466Xc 466Xd -466Xj, 466Xr, 471Yl, 482Xk, 491Mb, 491Xj, 491Xt, 495N\vfive{, - 521Rb, 524T, 524Xk, 524Zb, 525B, 525C, 528Xe, +466Xi, 466Xo, 471Yl, 482Xk, 491Mb, 491Xj, 491Xt, 495N\vfive{, + 521Rb, 524U, 524Xk, 524Zb, 524P, 525B, 528Xe, 535I, 531A, 531C, 531Xa, 533C, 543C, 543D, 544E, 544I, 544Xc, 546N, 547J}; %5 {\it see also} Haar measure ({\bf 441D}), @@ -11680,7 +11749,7 @@ \vtwo{quotient topology {\it 245Ba}\vfour{, {\it 443P-443S}, %{\it 443P}{\it 443Q}{\it 443R}{\it 443S} -{\it 443Xq}, {\it 443Yp}}%4 +{\it 443Xq}, {\it 443Yr}}%4 }%2 \indexmedskip%Ra @@ -11709,13 +11778,13 @@ 453Gb, 453K, 453Xf, {\it 453Za}, {\it 453Zb}, 454J, {\it 454K}, 454R, 454Sb, 457Mb, 462H-462K, %462H 462I 462J 462K -463M, 463N, 463Xi, 466A, 466O, 466Xk, 466Xl, 466Xq, 466Ya, 466Yd, +463N, 463Xi, 466A, 466Xj, 466Xp, 466Xq, 466Ya, 466Yc, 467Xj, 467Ye, 471F, 471Qb, 471Ta, 479W, 482Xc, 482Xe, 491Ma, 498B, 498Xa, 498Xb, 495Yd, 496Yd\vfive{, 524B, 524I-524K, %524I 524J 524K -524P, 524Q, 524S, -525D, 531Ad, 531F, 533D, 533G, 533H, 533J, 533Yd, 535K, +524Q, 524R, 524T, +525C, 531Ad, 531F, 533D, 533G, 533H, 533J, 533Yd, 535K, 544Xe, 552K, {\it 566S}, 566Xj, 567Xg}%5 }%4 @@ -11738,7 +11807,7 @@ }%4 \vtwo{Radon-Nikod\'ym derivative {\bf 232Hf}, 232Yj, -234J, 234Ka, 234Yi, 234Yj, 235Xh, 256J, 257F, 257Xe, 257Xf, +234J, 234Ka, 234Yi, 234Yj, 235Xh, 256J, 257F, 257Xe, 272Xe, 275Yb, 275Yj, 285Dd, 285Xe, 285Ya\vthree{, {\it 363S}\vfour{, @@ -11765,16 +11834,16 @@ 418M, 418Na, 418P, 418Q, 418Yk, 419E, 419Xb, 433I, 433Xg, 434Xe, 434Yp, 434Yt, 441Xa, 441Xd, 441Yb, 443U, 443Xs, -444Yd, 448P, 449A, 449E, 449Xq, 452Xd, 452Xe, 453L, 453N, 453Xi, 453Zb, +444Yd, 448P, 449A, 449E, 449Xr, 452Xd, 452Xe, 453L, 453N, 453Xi, 453Zb, 454M, 454N, 455E-455J, %455E {\it 455Fa} 455G 455H 455I 455J -455O, 455P, 455R, 455T, 455Xc, 455Xd, 455Xe, 455Xj, 455Xk, 455Yd, +455O, 455P, 455R, 455U, 455Xc, 455Xd, 455Xe, 455Xj, 455Xk, 455Yd, 456Aa, 457Lc, 457Xf, 457Xr, 458I, 458T, 458Xv, 458Xw, 459F, 459H, 459Xd, 459Xe, 461I, 461K-461P, %461K 461L 461M 461N 461O 461P -416Xe, {\it 461Xc}, 461Xj, 461Xl, {\it 461Yb}, 465U, 465Xb, 466Xb, 466Yc, +416Xe, {\it 461Xc}, 461Xj, 461Xl, {\it 461Yb}, 465U, 465Xb, 466Xb, 466Ye, 476C, 476I, 476K, 476Xe, 476Xf, 476Ya, 477B-477D, %477B 477C, 477D, 477Xd, 477Yd, 482Yc, -491Q, 491Xv, 491Xw, 491Yd, 491Yh, 491Yi, 493F, 498C, 498Xc, 498Xd, +491Q, 491Xv, 491Xw, 491Yd, 491Yh, 491Yi, 498C, 498Xc, 498Xd, 495Aa, 495N-495P, %495Nd 495O 495P 495Xo\vfive{, 524G, 524H, 524Xg, {\it 531D}, 532A-532C, %532A 532B 532C @@ -11833,7 +11902,7 @@ \vfour{\indexheader{rank}} \vfour{rank (of a tree) {\bf 421N}, 421O, 421Q, 423Ye\vfive{, - {\bf 562Ab}}%5 + {\bf 562Ac}}%5 }%4 \vfive{----- (of an element in a tree) {\bf 5A1Da} @@ -11961,7 +12030,7 @@ \vthree{\indexheader{reflexive}} \vthree{reflexive Banach space 372A, {\bf 3A5G}\vfour{, 449Ye, 461H, 461Yg, 467Xf\vfive{, - 537I, 561Xo, 567K}} %4%5 + 537I, 561Xr, 567K}} %4%5 }%3 %Reg @@ -11973,9 +12042,9 @@ \vtwo{\indexheader{regular}} \vfour{regular cardinal {\bf 4A1Aa}, 4A1Bc, 4A1Cc, 4A1I-4A1L\vfive{, %4A1Ic 4A1J 4A1K 4A1L - 513Bb, 513Ca, 513Ic, {\it 513Ya}, 514Dd, {\it 522Ub}, {\it 525L}, -541C, 541F-541I, %541F 541G 541H 541I -541K, 541M, 541P-541S, %541P 541Q 541R 541S + 513Bb, 513Ca, 513Ic, {\it 513Ya}, 514Dd, {\it 522Ub}, {\it 525K}, +541C, 541F-541I, %541F 541G 541H 541I +541K, 541M, 541P-541S, %541P 541Q 541R 541S 541Xa, 541Xd, 541Xg, 541Ya, 543Bb, 5A1Ac, 5A1E, 5A1N, 5A1O; {\it see also} weakly inaccessible cardinal ({\bf 5A1Ea})}%5 @@ -12039,7 +12108,7 @@ \indexiiiheader{regular open set} \vthree{regular open set {\bf 314O}, 314P, 314Q\vfour{, - 417Xt, 443N, {\it 443Yl}, 4A2Bj, 4A2Eb, 4A3R, 4A5Kb\vfive{, + 417Xt, 443N, {\it 443Yn}, 4A2Bj, 4A2Eb, 4A3R, 4A5Kb\vfive{, 514M, 514Xh}%5 }%4 }%3 @@ -12048,7 +12117,7 @@ }%3 regular outer measure 132C, {\bf 132Xa}\vtwo{, - {\it 213C}, 214Hb, 214Xb, 251Xn, 254Xb, 264Fb\vfour{, + {\it 213C}, {\it 213Xa}, 214Hb, 214Xb, 251Xn, 254Xb, 264Fb\vfour{, 471Dc, 471Yb}%4 }%2 @@ -12062,8 +12131,8 @@ 434Ib, 434Jc, {\it 437Ra}, 437Xm, 437Yn, {\it 437Yz}, {\it 438Yk}, {\it 462Aa}, {\it 462B}, {\it 496Xd}, 4A2F, 4A2H, 4A2Ja, 4A2N, 4A2Pb, 4A2Td, 4A3Xa\vfive{, - 514H, 514Jc, 516Ic, 561Xf, 561Xi, 561Xp, 561Xq, 561Yf, -562Bb, 562Xa, 562Xl, 563D, 563F, 563H, 563Xb, 563Xc}}; + 514H, 514Jc, 516Ic, 561Xg, 561Xj-561Xl, %561Xj, 561Xk 561Xl +562Cc, 562Xa, 562Xl, 563D, 563F, 563H, 563Xb, 563Xc}}; {\it see also} completely regular ({\bf 3A3Ad})}%3 }%2 @@ -12123,7 +12192,7 @@ \vtwo{relatively compact set $\pmb{>}${\bf 2A3Na}, 2A3Ob\vthree{, 3A3De, {\it 3A5I}, 3A5Nc\vfour{, 4A2Le, 4A2Ue\vfive{, - 561Xi}}}; %4%5%3 + 561Xj}}}; %4%5%3 {\it see also} relatively weakly compact }%2 @@ -12134,7 +12203,7 @@ \vfour{relatively independent family (in a measure algebra) {\bf 458L}\vfive{, - 525I}; %5 + 525H}; %5 (of measurable sets) {\bf 458Aa}, 458Yi, 485Lh }%4 @@ -12173,9 +12242,9 @@ \vtwo{relatively weakly compact set (in a normed space) 247C, {\bf 2A5Id}\vthree{, 356Q, 356Xl, 365Ua, {\it 3A5Gb}, 3A5Hb, {\it 3A5Lb}\vfour{, - 466Yd\vfive{, + 466Yc\vfive{, 566P, 566Q}}; %4%5 - (in other linear spaces) 376O, 376P, 376Xm\vfour{, 466Yd} %4 + (in other linear spaces) 376O, 376P, 376Xm\vfour{, 466Yc} %4 }%3 }%2 @@ -12191,16 +12260,21 @@ \indexheader{repeated} \vtwo{repeated integral \S252 ({\bf 252A})\vfour{, 417H, 434R, 436F, 436Xo\vfive{, - 537I-537L, %537I 537J 537K 537L -537N-537Q, %537N 537O 537P 537Q -537S, 537Xg, 537Xh, 537Xi, 538P, 538Xs, 538Yg, 538Yo, + 537I, 537J, 537L, 537Pb, +537S, 537Xg, 537Xi, 538P, 538Xs, 538Yg, 538Yo, 543C, 544C, 544I, 544Ja, 567Xf}}; %4%5 {\it see also} Fubini's theorem, Tonelli's theorem }%2 +\vfive{----- upper and lower integrals 537K, +537N-537Q, %537N 537O 537P 537Q +537Xi +}% + \indexheader{representation} -\vfour{representation (of a group) {\it see} finite-dimensional representation -({\bf 446A}), action ({\bf 441A}) +\vfour{representation (of a group) +{\it see} finite-dimensional representation ({\bf 446A}), +action ({\bf 441A}) }%4 \vfour{representation of an action 425D, 448S, 448T @@ -12208,14 +12282,14 @@ \vthree{representation of homomorphisms (between Boolean algebras) 344Ya, 344Yd, 364Q\vfour{, - 425A, 425D, 425E, 425Xc, 425Xd, 425Ya, 425Yb, 425Z\vfive{, + 425A, 425D, 425E, 425Xc, 425Xd, 425Ya, 425Z\vfive{, 5A6H}}; %5%4 (between measure algebras) 324A, 324B, 324N, 343A, 343B, 343G, 343J, 343M, 343Xc, 343Xg, 343Yd, 344A-344C, %344A 344B 344C 344E-344G, %344E 344F 344G 344Xf, 344Yc, 383Xk, 383Xl\vfour{, - 416Wb, 425Xg, 425Zc, {\it 451Ab}}%4 + 416Wb, 425Xg, 425Yb, 425Zc, {\it 451Ab}}%4 }%3 repn of B homos %Req%Rer%Res @@ -12231,13 +12305,13 @@ }%4 \indexvheader{resolvable} -\vfive{resolvable function {\bf 562O}, 562P, +\vfive{resolvable function {\bf 562Q}, 562R, 562Xg-562Xi, %562Xg 562Xh 562Xi -562Yc +562Yd }%5 -\vfive{----- set {\bf 562F}, 562G, 562H, -562O, 562Xa, 562Xb, 562Xd, 562Xe, 562Yb, 563Bb, 563C +\vfive{----- set {\bf 562G}, 562H-562J, %562H 562I, 562J, +562Q, 562Xa, 562Xb, 562Xd, 562Xe, 562Yc, 563Bb, 563C }%5 \indexheader{respects} @@ -12312,7 +12386,7 @@ 354Xc-354Xf, %354Xc, 354Xd, 354Xe, 354Xf, 354Xh, 354Yb, 354Yf, 354Yl, 355Xc, 356D, 356Xg, 356Xh\vfour{, {\it 437Qa}, {\it 438Xk}, 466H, 467Yb\vfive{, - 561Xk}}; %4%5 + 561Xn}}; %4%5 {\it see also} Fatou norm ({\bf 354Da}), order-continuous norm ({\bf 354Dc}), order-unit norm ({\bf 354Ga}) }%3 @@ -12330,7 +12404,7 @@ 241Yc, 241Yg\vthree{, chap.\ 35 ({\bf 352A}), 361Gc, 367C, 367Db, 367Xc, 367Xg, 367Yo\vfour{, 461O, 461P, 461Xk\vfive{, - 561Xk}}}; %3%4%5 + 561Xn}}}; %3%4%5 {\it see also}\vthree{ Archimedean Riesz space (\S352),} Banach lattice ({\bf 242G}\vthree{, {\bf 354Ab}}), Riesz norm ({\bf 242Xg}\vthree{, {\bf 354A}}) @@ -12339,7 +12413,7 @@ \vthree{Riesz subspace (of a partially ordered linear space) {\bf 352I}; (of a Riesz space) 352I, 352J, 352L, 352M, 353A, 354O, 354Rc\vfour{, - 461Xn, 4A2Jg}; %4 + 461Xn, 4A2Jh}; %4 {\it see also} band ({\bf 352O}), order-dense Riesz subspace ({\bf 352N}), solid linear subspace ({\bf 351I}) }%3 @@ -12358,11 +12432,12 @@ \vfour{right-translation-invariant lifting {\it 447Xa}, {\it 447Ya} }%4 -\vfour{right-translation-invariant metric 441Xq, 455P, 455R, 455T, +\vfour{right-translation-invariant metric 441Xq, 455P, 455R, 455U, {\bf 4A5Q} }%4 \rti -\vfour{right uniformity (of a topological group) 449B, 449D, 449E, 449H, +\vfour{right uniformity (of a topological group) 443Xj, +449B, 449D, 449E, 449H, 449Yc, {\bf $\pmb{>}$4A5Ha}, 4A5Mb, 4A5Q\vfive{, 534Xk, 534Ye}%5 }%4 @@ -12448,6 +12523,11 @@ \vtwo{saltus part of a function of bounded variation {\bf 226C}, 226Xb, 226Xc, 226Yd }%2 +\indexiiiheader{saturated} +\ifnum\volumeno<5 +\vthree{saturated {\it see} $\omega_1$-saturated ({\bf 316C}) +}%3 +\else \vfive{saturated {\it in} $\kappa$-saturated ideal (of a Boolean algebra) {\bf 541A}, 541B-541F, %541B 541C 541D 541E 541F 541J-541M, %541J 541K 541L 541M @@ -12456,19 +12536,29 @@ 541Xg, 555Q, 555Yb; {\it see also} $\omega_1$-saturated ({\bf 316C}) }%5 +\fi -\vfive{\indexheader{saturation} -saturation (of a Boolean algebra) {\bf 511Db}, 511I, 512Ec, 514Bb, +\indexvheader{saturation} +\vfive{saturation (of a Boolean algebra) {\bf 511Db}, 511I, 512Ec, 514Bb, 514D, 514E, 514Hb, 514J, 514K, -514Nc, 514Xb, 514Ye, 515F, 516La, 516Rb, 516Xk, 517Ig, 517Xe, {\it 525Dc}, -541A, 555Ya, 556Ec; - (of a pre- or partially ordered set) +514Nc, 514Xb, 514Ye, 515F, 516La, 516Rb, 516Xk, 517Ig, 517Xe, {\it 525Cc}, +541A, 555Ya, 556Ec +}%5 + +\vfive{----- (of a pre- or partially ordered set) {\bf 511B}, 511Db, 511H, 512Ea, 513B, 513Ee, -513Gc, 513Xh, 513Ya, 514Nc, 516Ka, 516T, 516Xe, 517F, 517G; - (of a forcing notion) 555Ya, {\bf 5A3Ad}; - (of a supported relation) {\bf 512Bb}, 512Dc, 512E, 512Xb, 512Ya, 513Yh, -516Ja; - (of a topological space) 512Eb, 514Bb, 514Hb, +513Gc, 513Xh, 513Ya, 514Nc, 516Ka, 516T, 516Xe, 517F, 517G +}%5 + +\vfive{----- (of a forcing notion) 555Ya, {\bf 5A3Ad} +}%5 + +\vfive{----- (of a supported relation) +{\bf 512Bb}, 512Dc, 512E, 512Xb, 512Ya, 513Yh, +516Ja +}%5 + +\vfive{----- (of a topological space) 512Eb, 514Bb, 514Hb, 514J, 514Nc, 516N, 516Qb, 516Xj, {\bf 5A4Ad}, 5A4B }%5 saturation @@ -12479,11 +12569,12 @@ }%2 \indexheader{scalarly} -\vfour{scalarly measurable {\bf 463Ya}\vfive{, {\bf 537H}, 537I}%5 +\vfour{scalarly measurable function {\bf 463Ya}\vfive{, +{\bf 537H}, 537I}%5 }%4 \indexheader{scattered} -\vfour{scattered topological space 439Ca, 439Xf, 439Xh, 439Xo, 466Xn, +\vfour{scattered topological space 439Ca, 439Xf, 439Xh, 439Xo, 466Xg, {\bf 4A2A}, 4A2G\vfive{, 531Ee, {\it 531N}}; %5 {\it see also} non-scattered @@ -12501,7 +12592,8 @@ }%2 \indexheader{Schwartz} -\vtwo{Schwartz function {\it see} rapidly decreasing test function ({\bf 284A}) +\vtwo{Schwartz function {\it see} rapidly decreasing test function +({\bf 284A}) }%2 \indexheader{Schwartzian} @@ -12515,9 +12607,9 @@ \vfour{second-countable topological space 411Yd, 415Xt, 418J, 434Ya, {\it 437Yn}, 454Yd, 495Ne, {\bf 4A2A}, 4A2O, 4A2P, 4A2Ua, 4A3G\vfive{, - 533Ca, 552Oa, 561Xc, {\it 561Yc}, 561Ye, 561Yf, + 533Ca, 552Oa, 561Xc, {\it 561Yc}, 561Yd, \S562, \S563, 564K-564O, %564K 564L 564M 564N 564O -564Xa, 564Xc, 565O, 567E, 567G, 5A4A, 5A4Da, 5A4H}%5 +564Xa, 564Xc, 565O, 567E, 567G, 5A4A, 5A4Da}%5 }%4 \vfour{Second Separation Theorem (of descriptive set theory) 422Yd @@ -12540,13 +12632,14 @@ \indexheader{self-adjoint} \vfour{self-adjoint linear operator 444Vc, {\bf 4A4Jd}, 4A4M\vfive{, - 561Xo}%5 + 561Xr}%5 }%4 \indexheader{self-supporting} -\vtwo{self-supporting set (in a topological measure space) {\bf 256Xf}\vfour{, +\vtwo{self-supporting set (in a topological measure space) +{\bf 256Xf}\vfour{, {\bf 411Na}, 414F, 415E, 415Xk, 416Dc, 416Xf, 417Ma, -443Xb, {\it 443Xk}, 443Yk, 456H\vfive{, +443Xb, {\it 443Xk}, 443Ym, 456H\vfive{, 532Hb}}%4%5 }%2 @@ -12561,7 +12654,7 @@ }%4 \indexheader{semi-continuous} -\vtwo{semi-continuous function\vfive{ 562Oa;}%5 +\vtwo{semi-continuous function\vfive{ 562Qa;}%5 {\it see\vfive {also}} lower semi-continuous ({\bf 225H}\vfour{, {\bf 4A2A}})\vfour{, upper semi-continuous ({\bf 4A2A})} }%2 @@ -12585,9 +12678,9 @@ }%3 semi-finite m alg \vtwo{semi-finite measure (space) {\bf 211F}, 211L, 211Xf, {\it 211Ya}, -{\it 212Ga}, 213A, 213B, 213Hc, 213Xc, 213Xd, 213Xj, 213Xl, 213Xm, -213Ya-213Yc %{\it 213Ya}, 213Yb, {\it 213Yc}, -213Yf, {\it 214Xd}, 214Xg, {\it 214Ya}, {\it 215B}, +{\it 212Ga}, 213A, 213B, 213Hc, 213Xc, 213Xd, 213Xh, 213Xl, 213Xm, +213Ya, 213Yb-213Yd %{\it 213Yb}, 213Yc, {\it 213Yd}, +{\it 214Xd}, 214Xg, {\it 214Ya}, {\it 215B}, {\it 216Xa}, {\it 216Yb}, 234B, 234Na, 234Xe, 234Xi, {\it 235M}, {\it 235Xd}, {\it 241G}, {\it 241Ya}, {\it 241Yd}, 243Ga, 245Ea, 245J, {\it 245Xd}, 245Xk, 245Xm, 246Jd, @@ -12618,7 +12711,10 @@ }%3 \indexiiheader{seminorm} -\vtwo{seminorm {\bf 2A5D}\vfour{, 4A4C, 4A4Da}%4 +\vtwo{seminorm {\bf 2A5D}, 2A5Ia\vthree{, + 3A5Ea\vfour{, + 4A4C, 4A4Da}}; %3%4 +{\it see also} F-seminorm ({\bf 2A5B}) }%2 \indexivheader{semi-radonian} @@ -12635,13 +12731,13 @@ 316Xo, 316Yj, 316Yk, 331O, 331Yj, 367Xr, 391Yc, {\bf 3A3E}\vfour{, 417Xt, 437Rc, 491H, 491Xv, 491Yi, 4A2Be, 4A2De, 4A2Ea, 4A2Ni, 4A2Oc, 4A4Bg\vfive{, - 524Xf, {\it 561Xc}, 561Xe, 567H, 5A4A}; + 524Xf, {\it 561Xc}, 561Xf, 567H, 5A4A}; {\it see also} hereditarily separable ({\bf 423Ya})}}%3%4 }%2 \vtwo{separable Banach space 244I, 254Yc\vthree{, 365Xp, 366Xc, 369Xg\vfour{, - 424Xe, 456Yd, 466M, 466O, 466Xe, 466Xq, 493Xe\vfive{, + 424Xe, 456Yd, 466M, 466O, 466Xe, 466Xp, 493Xf\vfive{, 564K}}}%4%5%3 }%2 @@ -12655,7 +12751,7 @@ 454Yd, 471Df, 471Xf, 4A2P, 4A2Tf, 4A2Ua, 4A3E, 4A3N, 4A3V, 4A4Id\vfive{, {\it 513M-513O}, %{\it 513M}{\it 513N}{\it 513O} {\it 522Va}, 527E, 532H, 532I, 535L, 535M, 535Xh, 537Hc, -546K, 561Ye, 566T, 566Xa, 566Yc, 567Xj, 5A4Bh, 5A4D}; %5 +546K, 561Yd, 566T, 566Xa, 566Yc, 567Xj, 5A4Bh, 5A4D}; %5 {\it see also} Polish space ({\bf 4A2A}) }%4 }%2 @@ -12718,7 +12814,7 @@ 561Xc, 566Xa}%5 }%4 -\vfive{sequentially complete metric space 561Xc, 561Xm +\vfive{sequentially complete metric space 561Xc, 561Xp }%5 \vfour{sequentially continuous function {\it 463B}, {\bf 4A2A}, 4A2Kd, 4A2Ld @@ -12732,7 +12828,7 @@ \vthree{\indexheader{sequentially order-continuous}} \vthree{sequentially order-continuous additive function (on a Boolean -algebra) 326Kc, 363Eb +algebra) 326Kc, 363Eb\vfour{, 448Yc}%4 }%3 \vthree{----- ----- Boolean homomorphism 313Lc, 313Pb, 313Qb, 313Xo, 313Ye, @@ -12751,7 +12847,7 @@ \vthree{----- ----- order-preserving function {\bf 313Hb}, 313Ic, 313Xg, 313Yb, 315D, -316Fc, 361Cf, 361Gb, 367Xb, 367Yc, 375Xd, 393Ba\vfour{, +316Fc, 361Cf, 361Gb, 361Xl, 367Xb, 367Yc, 375Xd, 393Ba\vfour{, 496A}%4 }%3 @@ -12809,13 +12905,13 @@ \vfive{\indexheader{Shelah}} \vfive{Shelah four-cardinal covering number $\covSh(\alpha,\beta,\gamma,\delta)$ 523Ma, 523Xd, -541S, 542D, {\bf 5A2Da}, 5A2E, 5A2G +541S, 542Dc, {\bf 5A2Da}, 5A2E, 5A2G }%5 \indexiiiheader{shift} -\vfour{shift action {\it 286C}, 425B, 425C, -441Yn, 443G, 443Xh, 443Xz, 443Yc, 444Of, 444Xq, 444Ym, -445H, 449D, 449E, 449Hb, 449J, 449Xk, +\vfour{shift action {\it 284Xd}, {\it 286C}, 425B, 425C, +441Yn, 443C, 443G, 443Xd, 443Xi, 443Xz, 443Yc, 444Of, 444Xq, 444Ym, +445H, 449D, 449E, 449Hb, 449J, 449Xl, 456Xc, 465Yi, {\bf 4A5Cc} }%4 @@ -12832,15 +12928,15 @@ }%3 \vfive{\indexheader{shrinking}} -\vfive{shrinking number of an ideal of sets {\bf 511Fb}, 511J, +\vfive{shrinking number of an ideal of sets {\bf 511Fc}, 511J, 521Ya, 523Ye, 544Ze; - {\it see also} augmented shrinking number ({\bf 511Fb}) + {\it see also} augmented shrinking number ({\bf 511Fc}) }%5 -\vfive{----- of a null ideal 511Xb-511Xe, %511Xb 511Xc 511Xd 511Xe +\vfive{----- of a null ideal 511Xc-511Xg, %511Xc 511Xd 511Xe 511Xf 511Xg 521C-521F, %521Cb 521Dd 521E 521Fb 521Ha, 521Xc, 523B, 523M, 523P, 523Xb, 523Xd, -523Ya, 523Yb, 523Ye, 523Z, 524Pe, 524Xg, 524Za, 552J, 555Yd +523Ya, 523Yb, 523Ye, 523Z, 524Qe, 524Xg, 524Za, 552J, 552Xf, 555Yd }%5 %Si @@ -12848,9 +12944,9 @@ \indexheader{Sierpi\'nski} Sierpi\'nski Class Theorem {\it see} Monotone Class Theorem (136B) -\vfive{Sierpi\'nski set {\bf 537Aa}, 537B, 537L, -537Xa-537Xc, %537Xa 537Xb 537Xc -537Xe, 537Za, 537Zb, 544G, 544Zb, {\it 567Xh}; +\vfive{Sierpi\'nski set {\bf 537Aa}, 537B, 537L, 537Xa, +537Xc-537Xf, %537Xc, 537Xd 537Xe 537Xf +537Za, 537Zb, 544G, 544Zb, {\it 567Xh}; {\it see also} strongly Sierpi\'nski set ({\bf 537Ab}) }%5 @@ -12943,7 +13039,7 @@ %Sm \indexheader{small} -\vfour{small subgroups {\it see} `no small subgroups' ({\bf 446E}) +\vfour{small subgroups {\it see} `no small subgroups' ({\bf 446G}) }%4 \vtwo{\indexheader{smooth}} @@ -13031,6 +13127,7 @@ }%5 \vfour{Souslin's operation \S421 ({\bf $\pmb{>}$421B}), 422Hc, 422Xc, +422Yg, 423E, 423M, 423N, 423Yb, 424Xg, 424Xh, 424Yc, \S431, 434D-434F, %434Dc 434Eb 434Fd 434Xn, 454Xe, 455Le, {\it 455M}, 471Dd, 496Ia\vfive{, @@ -13040,7 +13137,7 @@ %Sp \indexheader{space} -space-filling curve 134Yl +space-filling curve 134Yl\vtwo{, 254Yh\vfour{, 416Yi}} %2%4 \indexvheader{special} \vfive{special Aronszajn tree 553M, 553Yd, 554Yb, {\bf 5A1Dc} @@ -13058,7 +13155,7 @@ \indexiiheader{sphere} \vtwo{sphere, surface measure on 265F-265H, %265F, 265G, 265H, 265Xa-265Xc, %265Xa, 265Xb, 265Xc, -265Xe\vfour{, +265Xe, 265Xf\vfour{, 456Xb, 457Xl, {\it 476K}}%4 }%2 sphere @@ -13074,7 +13171,7 @@ 344Xf\vfour{, 419L, 419Xg-419Xi, %419Xg 419Xh 419Xi 419Yc, 424Yd, 452Xf, 433Xg, 434Ke, 434Yk, 438Ra, 438T, 438Xo, 438Xq, 453Xc, - 463Xg, 466Yc, 491Xh\vfive{, + 463Xg, 491Xh\vfive{, 524Xd, 527Xg, 531Xc, 533Xc}%5 }%4 }%3 split interval @@ -13116,7 +13213,7 @@ \indexivheader{standard} \vfour{standard Borel space \S424 ({\bf $\pmb{>}$424A}), 425A, 425D, 425E, 425Xa-425Xc, %425Xa, 425Xb, 425Xc -425Xf, 425Za, 433K, 433L, 433Yd, 448S, 451M, +{\it 425Xf}, 425Za, 433K, 433L, 433Yd, 448S, 448Xd, 448Yc, 451M, 452N, 452Xm, 454F, 454H, 454Xh, 4A3Wb }%4 % should this be `standard Borel structure'? @@ -13127,7 +13224,7 @@ }%3 \vfive{standard generating family (in the measure algebra of the usual -measure on $\{0,1\}^I$) {\it 331K}, {\bf 525A}, 525I +measure on $\{0,1\}^I$) {\it 331K}, {\bf 525A}, 525H }%5 \vtwo{standard normal distribution, standard normal random variable {\bf @@ -13143,7 +13240,7 @@ 541Lc, 541Ya, 542C, {\it 552L}, 5A1Ac, 5A1Gb, 5A1J, 5A1N}%5 }%4 -\vfour{stationary stochastic process {\bf 455Q}, {\bf 455Se} +\vfour{stationary stochastic process {\bf 455Q} }%4 \vfive{stationary-set-preserving partial order {\it 517Oe} @@ -13197,7 +13294,7 @@ 464P, {\bf 4A2I}\vfive{, 531Xd}; %5 (of $\Bbb N$) 416Yd, 434Yi\vfive{, - 532Xb, 538Yj, 5A4Ja}%5 + 532Xb, 538Yj, 5A4Ia}%5 }%4 Stone-Cech compactification \vfour{Stone's condition {\it see} truncated Riesz space ({\bf 436B}) @@ -13240,8 +13337,8 @@ \indexheader{stopping} \vtwo{stopping time {\bf 275L}, 275M-275O, %275M 275N 275O 275Xi-275Xk\vfour{, %275Xi, 275Xj, 275Xk - 455C, 455Ec, {\bf 455L}, 455M, 455O, 455S, 455T, -477G, 477I, 477Yg, 477Yh, 478Kb, 478Vb, 478Xb; + 455C, 455Ec, {\bf 455L}, 455M, 455O, 455U, +477G, 477I, 477Yg, 477Yh, 478Kb, 478Vb, 478Xb, {\it 479Xt}; {\it see also} hitting time, exit time}%4 }%2 @@ -13254,7 +13351,7 @@ }%4 \indexheader{strategy} -\vfour{strategy (in an infinite game) 451V, 4A2A\vfive{, +\vfour{strategy (in an infinite game) 451V\vfive{, {\bf 567A}; {\it see also} quasi-strategy ({\bf 567Ya}), winning strategy ({\bf 567Aa})}%5 @@ -13263,7 +13360,7 @@ \indexiiheader{strictly} \vtwo{strictly localizable measure (space) {\bf 211E}, 211L, {\it 211N}, 211Xf, -{\it 211Ye}, 212Gb, 213Ha, 213J, 213L, 213O, 213Xa, 213Xh, 213Xn, 213Ye, +{\it 211Ye}, 212Gb, 213Ha, 213J, 213O, 213Xa, 213Xj, 213Xn, 213Yf, 214Ia, 214K, 215Xf, {\it 216E}, 216Yd, 234Nd, {\it 235N}, 251O, 251Q, 251Wl, 251Xo, 252B, 252D, 252Yr, {\it 252Ys}\vthree{, @@ -13287,13 +13384,13 @@ }%3 \vfour{----- ----- measure (on a topological space) {\bf 411N}, 411O, -411Pc, 411Xh, 411Yd, 414P, 414R, +411Pc, 411Xh, 411Xk, 411Yd, 414P, 414R, {\it 415E}, {\it 415Fb}, {\it 415Xj}, {\it 416U}, 417M, 417Sc, {\it 417Yd}, {\it 417Yh}, {\it 418Xg}, 433Ib, 435Xj, 441Xc, 441Xh, 441Yk, -442Aa, 443Ud, {\it 443Yl}, 444Xn, 453D, 453I, 453J, 463H, 463M, 463Xd, +442Aa, 443Ud, {\it 443Yn}, 444Xn, 453D, 453I, 453J, 463H, 463M, 463Xd, 463Xk, 477F\vfive{, - 531B, 531Xn, 532E, 532F, 532Xf, 532Xd, 532Zc}%5 + 531B, 531Xn, 532E, 532F, 532Xd, 532Xf, 532Zc}%5 }%4 strictly positive measure \vthree{----- ----- submeasure (on a Boolean algebra) {\bf 392Ba}, 392F, @@ -13321,10 +13418,10 @@ {\it see also} almost strong lifting ({\bf 453A}) }%4 strong lifting -\vfive{strong limit cardinal 525O +\vfive{strong limit cardinal 525N }%5 -\vfour{strong Markov property 455O, 455T, 477G, 477Yf, 477Yg +\vfour{strong Markov property 455O, 455U, 477G, 477Yf, 477Yg }%4 \vthree{strong measure-algebra topology {\bf 323Ad}, 323Xg, 366Yi\vfour{, @@ -13369,7 +13466,7 @@ }%4 \vfive{strongly Sierpi\'nski set {\bf 537Ab}, 537B, 537F, -537Xa, 537Xb, 537Xf, 537Za, 552E; +537Xa, 537Xb, 537Za, 552E; {\it see also} Sierpi\'nski set ({\bf 537Aa}) }%5 @@ -13407,9 +13504,9 @@ }%4 \indexheader{subgroup} -\vfour{subgroup of a topological group 443Xf, 4A5E, 4A5Jb; - {\it see also} closed subgroup, compact subgroup, normal subgroup, -one-parameter subgroup +\vfour{subgroup of a group 443Xf, 4A5Bf, 4A5Cd, 4A5E, 4A5Jb; + {\it see also} closed subgroup, compact subgroup, normal subgroup +%one-parameter subgroup }%4 \indexivheader{subharmonic} @@ -13445,9 +13542,9 @@ \indexivheader{submodular} \vfour{submodular functional 132Xk, 413Xr, 413Yf, {\bf 432Jc}, 432L, -432Xj, 479E, 496Yd\vfive{, +432Xj, 475Xj, 479E, 496Yd\vfive{, 529Yb}%5 -}%4 432aA, 432aC +}%4 \indexiiiheader{subring} \vthree{subring {\bf 3A2C} @@ -13466,7 +13563,7 @@ 411Xg, 412O, 412P, 412Xq, {\it 413Xc}, 414K, 414Xn, 414Xp, 415B, 415J, 415Yb, 416R, 416T, 417I, 417Xf, {\it 435Xb}, 443K, 443Xf, 451Xg, 451Ya, 453E, 465C, 471E, 495Nc\vfive{, - 511Xb, 521D, 533Xb, 537Xd}}}} %5%4%3%2 + 511Xc, 511Xd, 521D, 533Xb, 537Xd}}}} %5%4%3%2 ----- ----- on a measurable subset 131A, {\bf 131B}, 131C, 132Xb, 135I\vtwo{, @@ -13505,7 +13602,7 @@ {\it 214Ce}\vfour{, {\it 418Ab}, 424Bd, 424E, 424G, 454Xd, 454Xf, 461Xg, 461Xi, 4A3Ca, 4A3Kd, 4A3Nd, 4A3Xh, 4A3Yb,\vfive{, - {\it 562D}, {\it 562Xj}}}}%4%5%2 + {\it 562E}, {\it 562Xj}}}}%4%5%2 \indexiiheader{substitution} \vtwo{substitution {\it see} change of variable in integration @@ -13554,7 +13651,7 @@ \indexheader{supermodular} \vfour{supermodular functional on a lattice {\bf 413P}, 413Xp, 413Yf, 496Yd -}%4 432aA, 432aC +}%4 \indexheader{support} \vthree{support of an additive functional on a Boolean algebra {\bf 326Xl} @@ -13564,7 +13661,7 @@ 381Sa, 381Xe, 381Xh, 381Xp, 382Ea, 382Ia, 382K, 382N, 382P-382R, %382P 382Q 382R 384B\vfour{, - {\it 494Ac}, {\it 494N}, 494Xh, {\it 494Yf}\vfive{, + {\it 494Ac}, {\it 494N}, 494Xh\vfive{, 556Ic, 566Xg}}%4%5 }%3 support of B homo @@ -13595,7 +13692,7 @@ automorphism) {\bf 381B}, 381E, 381Jb, 381Qb, 381Xm, 382D, 382N, 382O, 382Xl, 384B\vfour{, - {\it 494Ac}, 494Cb, {\it 494N}; }}%3%4 + {\it 494Ac}, 494Cb, {\it 494N}}; }%3%4 {\it see\vthree{ also}} self-supporting set ({\bf 256Xf}\vfour{, {\bf 411Na}}), support }%2 @@ -13618,10 +13715,10 @@ }%2 \vthree{symmetric difference (in a Boolean algebra) {\bf 311Ga}\vfour{, - 448Xj, 493D}%4 + 448Xi, 493D}%4 }%3 -\vfour{symmetric group 449Xg, 492H, 492I, 493Xb, 497F, 497Xb +\vfour{symmetric group 449Xh, 492H, 492I, 493Xb, 497F, 497Xb }%4 \vfour{symmetric Riemann-complete integral 481L @@ -13668,7 +13765,7 @@ }%3 \vfour{Talagrand's measure {\bf 464D}, 464E, 464N, 464R, 464Xb, 464Z, -466Xm +466Xr }%4 \indexivheader{Tamanini} @@ -13748,7 +13845,8 @@ 414Xj, 416Dd, 416N, 417C, 417E, 419D, 432Ca, 432Xc, 433Ca, 434A, {\it 434C}, {\it 434Gc}, {\it 434Ja}, 434Xb, 434Yr, 435Xb-435Xe, %435Xb {\it 435Xc} {\it 435Xd} 435Xe -436Xn, 436Yg, 451Sa, {\it 471I}, 471S, {\it 471Yc}, 476Ab, 476Xa\vfive{, +436Xn, 436Yg, 451Sa, 457Ye, +{\it 471I}, 471S, {\it 471Yc}, 476Ab, 476Xa\vfive{, 535N}; %5 {\it see also} Radon measure ({\bf 411Hb}), signed tight Borel measure ({\bf 437G}) @@ -13785,7 +13883,7 @@ \indexiiheader{topological} \vfour{topological group 383Xj, chap.\ 44, -455P-455T, %455P 455Q 455R 455Sf 455T +455P-455U, %455P 455Q 455R 455S 455U 455Yd, 494B, 494C, 494Yb, 494Yh, \S4A5 ({\bf 4A5Da}); {\it see also} abelian topological group, compact Hausdorff group, locally compact group, @@ -13801,7 +13899,7 @@ {\it 433A}, {\it 433B}, {\it 434Db}, {\it 461D}, 461F, 463H, 463Xd, {\it 464Z}, {\it 465Xj}, 471C, 471Da, 471Tb, 471Xf, 476A, 476E, 476Xa, 481N, 491R\vfive{, - 524Xf, 532D, 532E, 532Xf, 546K}; %5 + 521Xn, 524Xf, 532D, 532E, 532Xf, 546K}; %5 {\it see also} Borel measure ({\bf 411K}), quasi-Radon measure ({\bf 411Ha}), Radon measure ({\bf 411Hb})}%4 @@ -13837,7 +13935,7 @@ }%4 \vtwo{\indexheader{total}} -\vtwo{total order\vfour{ 418Xv\vfive{, 561Xr}; } +\vtwo{total order\vfour{ 418Xv\vfive{, 561Xd}; } {\it see\vfour{ also}} totally ordered set ({\bf 2A1Ac}) }%2 @@ -13855,10 +13953,10 @@ }%3 \indexheader{totally} -\vfour{totally bounded set (in a metric space) 411Yb, 434L, {\it 448Xi}, +\vfour{totally bounded set (in a metric space) 411Yb, 434L, {\it 448Xh}, 495Yd, {\bf 4A2A}\vfive{, 561Yc, 566Xa}; %5 - (in a uniform space) {\it 434Yh}, 443H, 443I, 443Xj, 443Ye, 463Xb, + (in a uniform space) {\it 434Yh}, 443H, 443I, 443Xj, 443Yg, 463Xb, {\bf 4A2A}, 4A2J, 4A5O }%4 @@ -13872,7 +13970,7 @@ 375Gb, 375I, {\it 383Fb}, 383I, 383J, 383Xg, {\it 383Ya}, 386Xa, 384O, {\it 384Xd}, 386A-386D, %386A 386C 386D 386K, 386Xd, 386Xf, 391B, 395R, {\it 396Xa}\vfour{, {\it 494Gd}\vfive{, - 525F, 525G, 525K, 525N, 525P, 525Ua, 528Xc}}%4%5 + 525E, 525F, 525J, 525M, 525O, 525Ta, 528Xc}}%4%5 }%3 tot fin m alg \vtwo{totally finite measure (space) {\bf 211C}, 211L, {\it 211Xb, 211Xc, 211Xd}, @@ -13928,7 +14026,7 @@ }%4 \indexheader{transitive} -\vfour{transitive action 442Z, 443U, 443Xy, 448Xi, 476C, 476Ya, {\bf 4A5Bb} +\vfour{transitive action 442Z, 443U, 443Xy, 448Xh, 476C, 476Ya, {\bf 4A5Bb} }%4 \indexheader{translation-invariant} @@ -14015,12 +14113,12 @@ \vfive{\indexheader{Tukey}} \vfive{Tukey equivalence {\bf 513D}, 513E, 513F, 513Xf, 513Xh, 514Xk, 522Xa, -522Yi, 524Ja, 525B, 526Hd, 529C, 529D, 529Xa, 529Xe +522Yi, 524Ja, 524P, 526Hd, 529C, 529D, 529Xa, 529Xe }%5 \vfive{Tukey function {\bf 513D}, 513E, 513N, 513O, 513Xc, 513Xe, 513Yb, 514Xa, 514Xd, 521Da, 521Fb, 521Hc, 522O, 522Yi, 524B, 524K, -524R, 525Xa, 526B, 526E, +524S, 525Xa, 526B, 526E, 526H-526L, %526Hc 526I 526J {\it 526K} {\it 526L} 526Xd, 529Ya, 534Bb, 534J, 539C, 539Ya; {\it see also} dual Tukey function ({\bf 513D}), @@ -14030,7 +14128,7 @@ %Tv%Tw \vfour{\indexheader{two-sided}} -\vfour{two-sided invariant mean 449Xn, 449Yd +\vfour{two-sided invariant mean 449J, 449Xo }%4 \vfive{\indexheader{two-valued-measurable}} @@ -14105,7 +14203,7 @@ }%3 \vfour{uniform convergence, topology of {\bf 4A2A}\vfive{, - 5A4I}%5 + 5A4H}%5 }%4 \vfour{uniform convergence on compact sets, topology of @@ -14116,7 +14214,7 @@ }%4 \vfour{uniform topology on a group $\AmuA$ -{\bf 494Ab}, 494C, 494O, 494Xb, 494Xg, 494Xh, 494Ya, 494Yf, 494Yj +{\bf 494Ab}, 494C, 494O, 494Xb, 494Xg, 494Xh, 494Ya, 494Yj }%4 %uniform filter 538Yd @@ -14140,28 +14238,29 @@ right uniformity ({\bf 4A5Ha})}, uniform space ({\bf 3A4A}) }%3 -\vfive{uniformity of an ideal of sets {\bf 511Fa}, 511J, 512Ed, 513Cb, +\vfive{uniformity of an ideal of sets {\bf 511Fb}, 511J, 512Ed, 513Cb, 526Xc, 527Bb, 534I, 539Ga }%5 \vfive{----- of an ideal of meager sets 522B, 522E, 522G, 522I, 522J, -{\it 522S}, 522U, 522Yf, 523Ye, 524Yc, 539Gb, 539Xb, 546O, 554Da, 554F +{\it 522S}, 522U, 522Yf, 522Yg, 523Ye, 524Yc, 539Gb, 539Xb, 546O, +554Da, 554F }%5 -\vfive{----- of a null ideal 511Xb-511Xe, %511Xb 511Xc 511Xd 511Xe +\vfive{----- of a null ideal 511Xc-511Xg, %511Xc 511Xd 511Xe 511Xf 511Xg 521D-521H, %521Db 521E 521Fa 521G 521Ha 521J, 521Xb-521Xd, %521Xb 521Xc 521Xd -521Xl, 522Va, 523B, 523Dd, 523H-523L, %523H 523I 523J 523K 523L +522Va, 523B, 523Dd, 523H-523L, %523H 523I 523J 523K 523L 523P, 523Xb, 523Xd, 523Ye, 523Yf, -524Jb, 524Me, 524Pd, 524Sb, 524Td, -525Hd, 534B, 534Za, 536Xb, 533Yb, 533Yc, 537Ba, 537N, 537Xh, +524Jb, 524Me, 524Qd, 524Tb, 524Ud, +525Gd, 534B, 534Za, 536Xb, 533Yb, 533Yc, 537Ba, 537N, 537Xh, 544H, 544Xf, 544Zc, 547Xd, 552H, 552Yb }%5 \vfive{----- of the Lebesgue null ideal 439F, 521G, 521Xb, 522B, 522E, 522G, 522S-522U, %{\it 522S} 522Td 522U -522Xb, 523Ia, 523J, 525L, 525Xc, 533Hb, 534Bd, 534Yc, 537Xg, 539Xb, +522Xb, 523Ia, 523J, 525K, 525Xc, 533Hb, 534Bd, 534Yc, 537Xg, 539Xb, 544Na, 547Xf, 552H, 552Ob }%5 %uniformity of Leb null ideal @@ -14178,7 +14277,7 @@ }%2 \vthree{uniformly convergent (sequence of functions) {\bf 3A3N}\vfour{, - 4A2Jg}%4 + 4A2Jh}%4 }%3 \vtwo{uniformly convex normed space 244O, 244Yn, {\bf 2A4K}\vthree{, @@ -14209,7 +14308,7 @@ \vtwo{uniformly integrable set (in $\eusm L^1$) \S246 ($\pmb{>}${\bf 246A}), 252Yo, 272Ye, 273Na, 274J, -275H, 275Xj, {\it 275Yp}, 276Xd, 276Yb\vfive{, +275H, 275Xj, {\it 275Yp}, 276Xe, 276Yb\vfive{, 538K, 538Yg}; %5 (in $L^1(\mu)$) \S246 ({\bf 246A}), 247C, 247D, 247Xe, 253Xd\vthree{, 354Q; @@ -14222,7 +14321,7 @@ }%3 }%2 unifly integrable -\vfour{uniformly Lipschitz family of functions {\bf 475Yf} +\vfour{uniformly Lipschitz family of functions {\bf 475Ye} }%4 \vfive{uniformly regular measure {\bf 533F}, 533G, 533H, @@ -14251,9 +14350,9 @@ \vfour{\indexheader{unimodular}} \vfour{unimodular topological group {\bf 442I}, -{\it 442Xf}, 442Yb, {\it 443Ag}, 443Xt, +{\it 442Xf}, 442Yb, {\it 443Ag}, 443Xn, 443Xt, 443Xv-443Xx, %443Xv 443Xw 443Xx -{\it 443Yr}, 444R, 444Yi, {\it 449Xd}, 449Yd +{\it 443Yt}, 444R, 444Yi, {\it 449Xd} }%4 \indexiiheader{unit} @@ -14305,7 +14404,7 @@ \vfour{----- ----- function {\bf $\pmb{>}$434D}, 434S, 434T, {\it 437Qa}, 437Xf, 463Zc, 464Yd, -466Xi, 478S, 478Xk\vfive{, +466Xl, 478S, 478Xk\vfive{, 538Q, 538Sb, 538Yp}%5 }%4 univ m'able fn @@ -14327,7 +14426,7 @@ {\it see also} $\Sigma_{\text{uRm}}$ ({\bf 434Eb}) }%4 -\vfour{----- ----- function {\bf 434Ec}, 437Ib, 466L\vfive{, 538Q}%5 +\vfour{----- ----- function {\bf 434Ec}, 437Ib, 463N, 466L\vfive{, 538Q}%5 }%4 \vfour{universally $\tau$-negligible topological space {\bf 439Xh}, 439Yd @@ -14391,8 +14490,7 @@ upper Riemann integral {\bf 134Ka} \vfour{upper semi-continuous function 414A, 471Xb, -471Xf, 476A, {\bf 4A2A}, -4A2Bd +471Xf, 476A, {\bf 4A2A}, 4A2Bd }%4 \vfour{----- ----- relation {\it 422A} @@ -14447,7 +14545,7 @@ %Uq%Ur \indexheader{Urysohn} -\vfour{Urysohn's Lemma 4A2F\vfive{, 561Xp, {\it 566Af}, 566U}%5 +\vfour{Urysohn's Lemma 4A2Fd\vfive{, 561Xl, {\it 566Af}, 566U}%5 }%4 \vfour{----- {\it see also} Fr\'echet-Urysohn ({\bf 462Aa}) @@ -14493,14 +14591,18 @@ 528J, 528K, 528N, 528Xa, 528Xg, 528Ya, 528Yh }%5 -\vtwo{\indexheader{variance}} -\vtwo{variance of a random variable {\bf 271Ac}, 271Xa, 272S, +\indexiiheader{variance} +\vtwo{variance (of a distribution) {\bf 271F}\vfour{, 455Xj, 455Yc}%4 +}%2 + +\vtwo{----- (of a random variable) {\bf 271Ac}, 271Xa, 272S, 274Ya, 274Yg, 285Gb, 285Xo }%2 \indexheader{variation} \vtwo{variation of a function \S224 ({\bf 224A}, {\bf 224K}, {\bf 224Yd}, -{\bf 224Ye}), 226B, 226Db, 226Xc, 226Xd, 226Yb, 226Yd, 264Xf, 265Yb\vfour{, +{\bf 224Ye}), 225Yg, 226B, 226Db, 226Xc, 226Xd, 226Yb, 226Yd, +264Xf, 265Yb\vfour{, 477Xh, 463Xi, 463Xj, 463Yc, 465Xc}; {\it see also} bounded variation ({\bf 224A}) }%2 variation of a function @@ -14531,9 +14633,9 @@ %Vf%Vg%Vh%Vi -\indexheader{Vietoris} +\indexivheader{Vietoris} \vfour{Vietoris topology 441Xo, 471Xb, 476Aa, {\bf 4A2Ta}\vfive{, - 513M, 513Xm, 513Xn, 5A4D}%5 + 513M, 513Xm, 513Xn, 561Xs, 5A4D}%5 }%4 \indexheader{virtually} @@ -14569,18 +14671,22 @@ %Vp%Vq%Vr%Vs%Vt%Vu%Vv%Vw%Vx%Vy%Vz \vtwo{\indexmedskip}%Wa -\indexheader{Wald} +\indexiiheader{Wald} \vtwo{Wald's equation 272Xh }%2 -\indexheader{wandering} +\indexiiiheader{wandering} \vthree{wandering {\it see} weakly wandering ({\bf 396C})\vfour{, few wandering paths ({\bf 478N})}%4 }%3 +\indexivheader{Wasserstein} +\vfour{Wasserstein metric {\bf 457K}, 457L, {\it 457Xo} +}%4 + %Wb%Wc%Wd%We -\indexheader{weak} +\indexiiheader{weak} \vfive{weak distributivity of a Boolean algebra {\bf 511Df}, 511I, 514Be, 514Dd, 514E, 514Hc, 514Jc, 514K, 514Xl, 517L, 524Mb, 526Yc, 528Xf, 533A, 539Ib @@ -14607,9 +14713,9 @@ 356Ye, 356Yf, 3A5E, 3A5Nd\vfour{, 436Xq, 462D-462F, %462D 462E 462F 462Xb, {\it 464Z}, {\it 465E}, 466B-466F, %466B 466C 466D 466E 466F -466H, 466Xe, {\it 466Xm}, 466Xn, 466Yc, 466Z, +466H, 466Xe, {\it 466Xr}, 466Xg, 466Za, 466Zb, 467Xg, 467Xh, 467Ye, 4A4K\vfive{, - {\it 525R}, 561Xo}%5 + {\it 525Q}, 561Xr}%5 }%4 }%3 }%2 weak topy of normed sp @@ -14631,7 +14737,7 @@ \vtwo{weak* topology on a dual space 253Yd, 285Yg, {\bf 2A5Ig}\vthree{, 3A5E, 3A5F\vfour{, 437K, {\bf 4A4Bd}, 4A4If\vfive{, - 561Xg}}}; %3%4%5 + 561Xh}}}; %3%4%5 {\it see also} vague topology ({\bf 274Ld}\vfour{, {\bf 437J}}) }%2 @@ -14649,7 +14755,7 @@ \vtwo{weakly compact set (in a linear topological space) 247C, 247Xa, 247Xc, 247Xd, {\bf 2A5I}\vthree{, {\it 376Yj}\vfour{, - 461J, 462E, 462G, 466Yd, {\it 4A4F}, 4A4Ka\vfive{, + 461J, 462E, 462G, 466Yc, {\it 4A4F}, 4A4Ka\vfive{, 566Xe, 566Xf, 566Yd}}}; %3%4%5 {\it see also}\vfour{ Eberlein compactum ({\bf 467O}),} relatively weakly compact ({\bf 2A5Id}) @@ -14673,7 +14779,8 @@ 467M, 467Xc, 467Xh, 467Ya }%4 -\vfour{weakly measurable function {\it see} scalarly measurable ({\bf 463Ya}) +\vfour{weakly measurable function {\it see} scalarly measurable +({\bf 463Ya}) }%4 \vthree{weakly mixing \imp\ function {\bf 372Ob}, 372Qb, {\it 372Xr}, @@ -14682,7 +14789,8 @@ \vthree{weakly mixing measure-preserving Boolean homomorphism {\bf 372Oa}, 372Qa, 372Rd, 372Xo, 372Xy, 372Yi, 372Yn, 372Ys\vfour{, - 494D, 494E, 494F, 494Xi, 494Xj, 494Yg}%4 + 494D-494F, %494D, 494E, 494Fc, +494Xi, 494Xj, 494Yg}%4 }%3 \vthree{weakly von Neumann automorphism {\bf 388D}, 388F, 388H, 388Xd, 388Yc @@ -14733,11 +14841,11 @@ }%3 \vfive{weakly $(\kappa,\infty)$-distributive Boolean algebra {\bf 511Df}, -511Xm; +511Xn; {\it see also} weak distributivity ({\bf 511Df}) }%5 -\vfive{----- ----- Riesz space {\bf 511Xm} +\vfive{----- ----- Riesz space {\bf 511Xn} }%5 \indexheader{Weierstrass} @@ -14751,8 +14859,8 @@ 514Ba, 524Xf, 527Yc, 531A, 531Ba, 531Ea, 531H, 531Xe-531Xg, %531Xe 531Xf 531Xg 533C-533E, %533C 533D 533E -{\it 536Cc}, 539Ib, 543C, 543D, 544E, 544I, 544J, 544Xc, 544Za, 566Ae, -{\bf 5A4Aa}, 5A4B, 5A4C, 5A4Ja}; +{\it 536Dc}, 539Ib, 543C, 543D, 544E, 544I, 544J, 544Xc, 544Za, 566Ae, +{\bf 5A4Aa}, 5A4B, 5A4C, 5A4Ia}; {\it see also} measure-free weight\vfive{, network weight ({\bf 5A4Ai}), $\pi$-weight ({\bf 5A4Ab})}%5 }%4 weight @@ -14768,13 +14876,13 @@ \indexvheader{well-orderable} \vfive{well-orderable set {\bf 561A}, {\it 561D-561F}, %{\it 561D}{\it 561E}{\it 561F} -561Xj, {\it 561Yj}, 567B +561Xm, 561Yd, 567B }%5 \indexiiheader{well-ordered} \vtwo{well-ordered set 214P, {\bf 2A1Ae}, 2A1B, 2A1Dg, 2A1Ka\vfour{, 4A1Ad, 4A2Rk,\vfive{ - 561A, 561Xr, 5A1Da}}; %4%5 + 561A, 561Xd, 5A1Da}}; %4%5 {\it see also} ordinal ({\bf 2A1C}) }%2 @@ -14854,8 +14962,8 @@ \vthree{zero-dimensional topological space 311I-311K, %311I 311J 311K 315Xh, 316Xq, 316Yc, 353Yc, {\bf 3A3Ae}, 3A3Bd\vfour{, {\it 414R}, 416Qa, {\it 419Xa}, 437Xi, {\it 481Xh}, -482Xc, 491Ch, 496F, 4A2Ud, 4A3Oe\vfive{, - 535L, {\it 546N}, 5A4J}}%4%5 +482Xc, 491Ch, 496F, 4A2Ud, 4A3I, 4A3Oe\vfive{, + 535L, {\it 546N}, 5A4I}}%4%5 }%3 zero-dimensional topological space \vtwo{zero-one law 254S, 272O, 272Xf, 272Xg\vthree{, @@ -14864,12 +14972,12 @@ }%3 }%2 -\vfour{zero-one metric 441Xq, 449Xg, 493Xb +\vfour{zero-one metric 441Xq, 449Xh, 493Xb }%4 \vthree{zero set in a topological space {\it 313Ye}, {\it 316Yh}, {\it 324Yb}, {\bf 3A3Qa}\vfour{, - 411Jb, 412Xh, {\it 416Xj}, 421Xg, 423Db, 443N, 443Yk, 443Yn, + 411Jb, 412Xh, {\it 416Xj}, 421Xg, 423Db, 443N, 443Ym, 443Yo, {\it 491C}, 4A2Cb, 4A2F, 4A2Gc, 4A2Lc, 4A2Sb, 4A3Kd, 4A3Nc, 4A3Xc, 4A3Xf, 4A3Yb\vfive{, 532B, 532H, 532Xa, 532Ya, 533D, {\it 533Ga}, 5A4Ed}}%4%5 @@ -14903,7 +15011,7 @@ \vfive{$\add$ (in $\add P$) {\it see} additivity of a pre-ordered set ({\bf 511Bb}); - (in $\add\mu$) {\it see} additivity of a measure ({\bf 511G}); + (in $\add\mu$) {\it see} additivity of a measure ({\bf 511Ga}); (in $\add(A,R,B)$) {\it see} additivity of a supported relation ({\bf 512Ba}) }%5 @@ -14937,7 +15045,7 @@ 444Yh\vfive{, 538K}}; %4%5 ($\eurm B(U;U)$) 396Xb\vfour{, 4A6C; - ($\eurm B(\BbbR^r,\BbbR^r)$) 446A}} %3%4 + ($\eurm B(\BbbR^r,\BbbR^r)$) 446Aa}} %3%4 }%2 \vfour{$\Cal B$ (in $\Cal B(X)$) {\it see} Borel $\sigma$-algebra @@ -14945,7 +15053,7 @@ }%4 \vfive{$\Cal B_c$ (in $\Cal B_c(X)$) {\it see} codable Borel set -({\bf 562Ag}) +({\bf 562Bd}) }%5 \vfour{$\widehat{\Cal B}$ (in $\widehat{\Cal B}(X)$) {\it see} @@ -14953,7 +15061,7 @@ }%4 \vfour{$B$-sequence (in a topological group) {\bf 446L}, 446M, 446N, 446P, -446Xc, 447C, 447D, 447F, 447Xb, 447Xc +446Xb, 447C, 447D, 447F, 447Xb, 447Xc }%4 \vfour{$\CalBa$ (in $\CalBa(X)$) {\it see} Baire $\sigma$-algebra ({\bf @@ -14962,7 +15070,7 @@ }%4 \vfive{$\CalBa_c$ (in $\Cal Ba_c(X)$) {\it see} codable Baire set -({\bf 562R}) +({\bf 562T}) }%5 \vfive{$\bu$ (in $\bu P$) {\it see} bursting number ({\bf 511Bj}) @@ -14989,7 +15097,7 @@ {\bf 2A1L}, 2A1P\vthree{, {\it 343I}, {\it 343Yb}, 344H, {\it 383Xd}\vfour{, {\it 416Yg}, 419H, 419I, -419Xd, 421Xc, 421Xh, 421Yd, 423K, 423Xh, {\it 423Ye}, 424Db, 425E, +419Xd, 421Xc, 421Xh, 421Yd, 423K, 423Xh, {\it 423Ye}, 424Db, {\it 425E}, 434Xg, {\it 436Xg}, 438C, 438T, 438Xq-438Xs, %438Xq 438Xr 438Xs 438Yb, 438Yc, 438Yh, 439P, {\it 439Xn}, 454Yb, 466Zb, @@ -14997,11 +15105,11 @@ 4A1A, 4A1O, 4A2Be, 4A2De, 4A2Gj, 4A3F\vfive{, 517O, 517Pa, 517Rb, 521L, 521Nb, 521Xf, 521Yb, 522B, 522F, 522Td, 522Ua, 523Jc, 523Kb, -524Yb, 525Xc, 527H, 528Yf, 528Yh, 534Zd, 535Lc, 535Xk, 539Pfg, 542C, +524O, 524Yb, 525Xc, 527H, 528Yf, 528Yh, 534Zd, 535Lc, 535Xk, 539Pfg, 542C, {\it 542E-542G}, %{\it 542E}{\it 542F}{\it 542Ga} -542O, 543B, 543Xc, 544Yb, 544Zc, 544Zf, +543B, 543Xc, 544Yb, 544Zc, 544Zf, {\it 545A}, 545C, 546Ce, {\it 547Xf}, -552Gc, 552Xd, 553O, 554F, 554I, 555Xb, 555Xc, 5A1Ee, 5A1Fc, 5A4Ja}; %5 +552Gc, 552Xd, 553O, 554F, 554I, 555Xb, 555Xc, 5A1Ee, 5A1Fc, 5A4Ia}; %5 {\it see also}\vfive{ axiom,} continuum hypothesis\vfive{, $2^{\frak c}$}}}%3%4%5 }%2 \frak c @@ -15020,56 +15128,75 @@ 416Xj, 416Yg, 424Xf, 436Xe, 436Xg, 437Yt, 454Q-454S, %454Q 454R 454S 454Xl, 454Xm, 462C, 462I, 462J, 462L, 462Ya, 462Yd, 462Z, -463Xd, 466Xf, 466Xn, 466Yc, 467Pa, 467Ye, 477Yb, +463Xd, 466Xf, 466Xg, 467Pa, 467Ye, 477Yb, 4A2Ib, 4A2N-4A2P, %4A2Nj 4A2Oe 4A2Pe 4A2Ue\vfive{, 531Yb, 533Xd}}}; %4%3%5 (in $C([0,1])$) 242 {\it notes}\vthree{, 352Xg, 356Xb, 368Yf\vfour{, 436Xi, 436Xm, 437Yc, 437Yt, 462Xd}; (in $C(X;\Bbb C)$) 366M\vfour{, 437Yb; - (in $C(X;Y)$) 4A3Wd\vfive{, 546N, 5A4I}; %5 + (in $C(X;Y)$) 4A3Wd\vfive{, 546N, 5A4H}; %5 (in $C(\coint{0,\infty};\BbbR^r)_0$) 477B-477L ({\bf 477D}), %477B 477C 477D 477E 477F 477G 477H 477I 477J 477K 477L 477Xb, 477Xh, 477Ya, 477Yc-477Ye, %477Yc, 477Yd, 477Ye, -477Yh, 477Yj, 4A2Ue - }}%4%5%3 +477Yh, 477Yj, 4A2Ue}}%4%5%3 }%2 % C(X) % Aviles Plebanek & Rodriguez p11 +\vtwo{$C_b$ (in $C_b(X)$, where $X$ is a topological space) {\bf 281A}, +281E, 281G, 281Ya, 281Yd, 281Yg, 285Yg\vthree{, + 352Xj, 352Xk, 353Yb, {\bf 354Hb}, 363A, 363Y\vfour{, + {\it 418Xp}, 436E, 436I, 436L, 436Xf, 436Xl, 436Xn, 436Xs, 436Yc, +437E, 437J, 437K, 437Xe, {\it 437Yf}, 437Ym, 437Yp, +444E, 444I, 444R, 444S, 449J, 453Cb, 459Xc, 462F-462H, %462F, 462G 462H +462Xb, 463H, 483Mc, 491C, 491O, 491Ye, 491Yf, {\bf 4A2A}\vfive{, + 561Xb, 564H, 564Xb}}}; %3%4%5 + (in $C_b(X;\Bbb C)$) 281G, 281Yg +}%2 + +\vfour{$\Cdlg$ {\it see} \cadlag\ function ({\bf 4A2A}) +}%4 + +\vtwo{$C_k$ (in $C_k(X)$, where $X$ is a topological space) +242O, 244Hb, 244Yj, 256Xh\vfour{, + 416I, 416Xk, 436J, 436Xo, 436Xs, 436Yg, 443P, 495Xl, 4A5P\vfive{, + 561G, 564I, 565I, 566Xj}}; %4%5 + {\it see also} compact support +}%2 + +\vtwo{----- (in $C_k(X;\Bbb C)$) 242Pd +}%2 + \vfour{$C_0$ (in $C_0(X)$, where $X$ is a topological space) {\bf 436I}, 436K, 436Xq, 437I, 437Ye, 443Yc, {\it 445K}, 449Ba, 462E, {\it 464Yc}, 4A6B }%4 -\vfive{$c_0$ (in $c_0(X)$) 538Ai -}%5 - -\vthree{$C^{\infty}$ (in $C^{\infty}(X)$, for extremally disconnected $X$) -{\bf 364V}, 364Ym, 368G -}%3 - \vthree{$\pmb{c}$ (the space of convergent sequences) {\bf 354Xq}, 354Xs, 355Ye }%3 -\vthree{$\pmb{c}_0$ 354Xa, 354Xd, 354Xi, 371Yc\vfour{, 461Xc, 464Yc; +\vthree{$\pmb{c}_0$ 354Xa, 354Xd, 354Xi, 371Yc\vfour{, 461Xc; {\it see also} $\ell^{\infty}/\pmb{c}_0$ }%4 }%3 -\vthree{cac (`countable antichain condition') 316 {\it notes} +\vfour{----- (in $c_0(X)$) 464Yc\vfive{, 538Ai}%5 +}%4 + +\vthree{$C^{\infty}$ (in $C^{\infty}(X)$, for extremally disconnected $X$) +{\bf 364V}, 364Ym, 368G }%3 -\vtwo{$C_b$ (in $C_b(X)$, where $X$ is a topological space) {\bf 281A}, -281E, 281G, 281Ya, 281Yd, 281Yg, 285Yg\vthree{, - 352Xj, {\bf 354Hb}\vfour{, - 436E, 436Ia, 436L, {\it 436Xf}, 436Xl, 436Xs, 436Yc, -437J, 437Xe, 437Yp, 449J, 462F-462H, %462F 462G 462H -462Xb, 483Mc, 491C\vfive{, - 561Xb, 564H, 564Xb}}%4%5 - }%3 -}%2 C_b(X) +\vfour{$\Clll$ {\it see} \callal\ function ({\bf 4A2A}) +}%4 + +\vfour{$\tildeClll$ (in $\tildeClll(X)$) 438P, 438Q, 462Ye +}%4 + +\vthree{cac (`countable antichain condition') 316 {\it notes} +}%3 \vthree{ccc Boolean algebra {\bf 316Aa}, 316B-316F, %316B 316C 316D 316E 316F @@ -15084,7 +15211,7 @@ 425Ad, 431G, {\it 448Ya}, 496Bb\vfive{, 511Id, 514Yf, 514Yg, 515M, 516U, {\it 527M}, 527O, 527Yb, 539K-539P, %539K 539L 539M 539N 539O -539Yb, 546Ce, 546Xa, 555Jc, 555M}}%5%4 +539Yb, 546Ce, 546Xa, 555Jc, 555M, {\it 561Yc}}}%5%4 }%3 % ccc B alg @@ -15103,9 +15230,6 @@ 546E, 546F, {\it 561Yc}, 5A4A, 5A4Ed}}%5%4 }%3 -\vfour{$\Cdlg$ {\it see} \cadlag\ function ({\bf 4A2A}) -}%4 - \vthree{$\cf$ (in $\cf P$) {\it see} cofinality ({\bf 3A1Fb}\vfive{, {\bf 511Ba}}) }%3 @@ -15113,16 +15237,6 @@ \vfive{$\ci$ (in $\ci P$) {\it see} coinitiality ({\bf 511Bc}) }%5 -\vtwo{$C_k$ (in $C_k(X)$, where $X$ is a topological space) -242O, 244Hb, 244Yj, 256Xh\vfour{, - 416I, 416Xk, 436J, 436Xo, 436Xs, 436Yg, 443P, 495Xl, 4A5P\vfive{, - 561G, 564I, 565I, 566Xj}}; %4%5 - {\it see also} compact support -}%2 - -\vtwo{----- (in $C_k(X;\Bbb C)$) 242Pd -}%2 - \vfive{CL {\it see} Jensen's Covering Lemma ({\bf 5A6Bb}) }%5 @@ -15150,7 +15264,7 @@ \vtwo{c.l.d.\ version of a measure (space) {\bf 213E}, 213F-213H, %213F, 213G, 213H, 213M, 213Xb-213Xe, %213Xb 213Xc 213Xd 213Xe -213Xg, 213Xj, 213Xk, 213Xn, 213Xo, 213Yb, {\it 214Xe}, 214Xi, {\it 232Ye}, +213Xg, 213Xi, 213Xn, 213Xo, 213Yc, {\it 214Xe}, 214Xi, {\it 232Ye}, 234Xl, 234Yj, 234Yo, 241Ya, 242Yh, {\it 244Ya}, 245Yc, 251Ic, 251T, 251Wf, 251Wl, 251Xe, 251Xk, 251Xl, 252Ya\vthree{, @@ -15159,22 +15273,16 @@ 411Xc, 411Xd, 412H, 413Eg, 413Xj, 413Xm, {\it 414Xj}, {\it 415Xn}, 416F, 416H, 436Xa, {\it 436Xc}, {\it 436Xk}, {\it 436Yd}, 451G, 451Yn, 465Ci, 471Xh, 471Yi, 491Xr\vfive{, - 511Xd, 511Yc}%5 + 511Xe, 511Yc}%5 }%4 }%3 }%2 c.l.d. version -\vfour{$\Clll$ {\it see} \callal\ function ({\bf 4A2A}) -}%4 - -\vfour{$\tildeClll$ (in $\tildeClll(X)$) 438P, 438Q, 462Ye -}%4 - \vfour{$\clstar$ {\it see} essential closure ({475B}) }%4 \vfive{$\cov$ (in $\cov(X,\Cal I)$, $\cov\Cal I$) -{\it see} covering number ({\bf 511Fc}) +{\it see} covering number ({\bf 511Fd}) }%5 \vfive{$\covSh$ (in $\covSh(\alpha,\beta,\gamma,\delta)$) {\it see} @@ -15200,10 +15308,11 @@ {\it see} centering number ({\bf 511Bg}) }%5 -\vthree{$D$ (in $D_n(A,\pi)$, where $A$ is a subset of a Boolean algebra, and $\pi$ is a homomorphism) {\bf 385K}, 385L, {\it 385M}\vfour{; +\vthree{$D$ (in $D_n(A,\pi)$, where $A$ is a subset of a Boolean algebra, +and $\pi$ is a homomorphism) {\bf 385K}, 385L, {\it 385M}\vfour{; (in $D_n(A)$, where $A$ is a subset of a topological group) {\bf 446D}; - (in $D_k(A,E,\alpha,\beta)$, where $E$ is a set and $A$ is a set of functions) -{\bf 465Ae} + (in $D_k(A,E,\alpha,\beta)$, where $E$ is a set and $A$ is a set of +functions) {\bf 465Ae} }%4 }%3 @@ -15267,9 +15376,14 @@ \vthree{$^f$ (in $\frak A^f$) {\bf 322Db} }%3 -\vfour{F$_{\sigma}$ set {\it 412Xg}, 414Yd, {\it 443Jb}, {\it 466Yb}, +\vtwo{F-seminorm 245D, {\bf 2A5B}, 2A5C, 2A5D, 2A5G\vthree{, + 366Ya, 3A4Bd\vfour{, + 463A}} %34 +}%2 + +\vfour{F$_{\sigma}$ set {\it 412Xg}, 414Yd, {\it 443Jb}, {\it 466Yd}, {\bf 4A2A}, 4A2Ca, 4A2Fi, {\it 4A2Ka}, {\it 4A2Lc}\vfive{, - 562Ca, 562Xa, 562Yb, 562Yc, 563Xb}%5 + 562Da, 562Xa, 562Yc, 562Yd, 563Xb}%5 }%4 \vfour{F$_{\sigma\delta}$ set {\bf 475Yg} @@ -15307,7 +15421,7 @@ ({\bf 511Bi}) }%5 -\vfive{$\FN^*(\Cal P\Bbb N)$ 525Q, 526Ye +\vfive{$\FN^*(\Cal P\Bbb N)$ 525P, 526Ye }%5 \vtwo{\indexmedskip}%$G @@ -15319,7 +15433,7 @@ {\it 434Xb}, 437Ve, 437Yy, {\it 443Jb}, 461Xj, 471Db, 494Ec, {\it 494Xf}, {\bf 4A2A}, 4A2C, 4A2Fd, 4A2K-4A2M, %4A2Kf 4A2L 4A2Mc 4A2Q, 4A5R\vfive{, - {\it 526Xe}, 532Xd, 562Ca, 562Yb, 563Xb, 5A4Ca, 5A4Je}}}%3%4%5 + {\it 526Xe}, 532Xd, 562Da, 562Yc, 563Xb, 5A4Ca, 5A4Ie}}}%3%4%5 }%2 \vfour{G$_{\delta\sigma}$ set {\bf 475Yg} @@ -15328,7 +15442,7 @@ \vfive{GCH {\it see} generalized continuum hypothesis ({\bf 5A6A}) }%5 -\vfour{$GL(r,\Bbb R)$ (the general linear group) {\bf 446A} +\vfour{$GL(r,\Bbb R)$ (the general linear group) {\bf 446Aa} }%4 \vfour{$\grad f$ {\it see} gradient ({\bf 473B}) @@ -15398,7 +15512,7 @@ \vfour{K-analytic set, topological space {\bf 422F}, 422G-422K, %422G, 422H, 422I, 422J 422K 422Xb-422Xf, %422Xb 422Xc 422Xd 422Xe 422Xf -422Ya, 422Yb, 422Yd-422Yf, %422Yd 422Ye 422Yf, +422Ya, 422Yb, 422Yd-422Yg, %422Yd 422Ye 422Yf 422Yg 423C-423E, %423C, 423D, 423E, \S432, 434B, 434Dc, 434Jf, 434Ke, 434Xq, 434Xr, {\it 435Fb}, 436Xe, 437Rd, 438Q, 438S, @@ -15452,7 +15566,8 @@ \vtwo{$\ell^{\infty}$ (in $\ell^{\infty}(X)$) {\bf 243Xl}, {\bf 281B}, 281D\vthree{, 354Ha, 354Xa, 361D, 361L\vfour{, - 461Xd, 464F, 464R, 464Xb, 464Z, 466I, 466Xm, 466Z, {\it 483Yj}, 4A2Ib}%4 + 461Xd, 464F, 464R, 464Xb, 464Z, 466I, 466Xr, 466Za, +{\it 483Yj}, 4A2Ib}%4 }%3 }%2 ell^{\infty} @@ -15483,7 +15598,7 @@ 371Xa, 371Xb, 371Xf, 371Ya, 376Mb, 376P, 376Yj, 377Yc, 377Yd\vfour{, 436Ib, 436Yb, 437B, 437C, 437E, 437F, 437H, 437I, 437Yc, 437Yi, {\it 444E}, {\it 461Q}, 461Xn, 467Yb, 495K, 495Ya, 495Yb\vfive{, - 529C, 529Xb, 561H, 561Xl, 564K, 566Q, 566Xf, 566Ya, 567K}};%4%5 + 529C, 529Xb, 561Hb, 561Xo, 564K, 566Q, 566Xf, 566Ya, 567K}};%4%5 {\it see also} $M(\frak A)$ }%3 L-space @@ -15523,9 +15638,9 @@ \S369, {\it 372C}, \S375, 376B, 376Yb, 377B-377F, %377B 377C 377D 377E 377F 377Xa, 393K, 393Yc, 393Yd, 395I\vfour{, - 443A, 443G, 443Jb, 443Xh, 443Yt, 443Yu\vfive{, + 443A, 443G, 443Jb, 443Xh, 443Ye, 443Yf\vfive{, 515Mb, 518Yc, 529Bb, 529D, 538Ka, 551B, 556Af, 556H, 556K, 556Lb, -561H, 566O, 5A3L, 5A3M}}; %4%5 +561Ha, 566O, 5A3L, 5A3M}}; %4%5 }%3 \vthree{----- (in $L^0_{\Bbb C}(\frak A)$) {\bf 366M}, @@ -15536,7 +15651,8 @@ \vtwo{----- {\it see also} $\eusm L^0$ ({\bf 241A}\vthree{, {\bf 364B}}) }%2 L^0 -$\eusm L^1$ (in $\eusm L^1(\mu)$) {\it 122Xc}\vtwo{, 242A, 242Da, 242Pa, 242Xb\vfour{, +$\eusm L^1$ (in $\eusm L^1(\mu)$) {\it 122Xc}\vtwo{, 242A, 242Da, 242Pa, +242Xb\vfour{, 443Q, 444P-444R\vfive{, %444P 444Q 444R {\bf 564Ad}, 564Ba, 564C, 564E, 564G, 564J, 565Ia}}; %5%4 (in $\eusm L^1_{\Sigma})$ {\bf 242Yg}\vthree{, 341Xg}; @@ -15545,7 +15661,9 @@ {\it see also} $L^1$, $\|\,\|_1$ }%2 -\vtwo{$L^1$ (in $L^1(\mu)$) \S242 ({\bf 242A}), {\it 243De}, 243F, 243G, 243J, 243Xf-243Xh, %243Xf, {\it 243Xg}, {\it 243Xh}, +\vtwo{$L^1$ (in $L^1(\mu)$) \S242 ({\bf 242A}), +{\it 243De}, 243F, 243G, 243J, 243Xf-243Xh, %243Xf, {\it 243Xg}, +{\it 243Xh}, 245H, 245J, 245Xh, 245Xi, \S246, \S247, \S253, 254R, 254Xp, 254Ya, 254Yc, 257Ya, {\it 282Bd}\vthree{, 323Xb, 327D, 341Xg, 354M, 354Q, 354Xa, 365B, 376N, 376Q, 376S, @@ -15564,7 +15682,7 @@ 372G, 372Xc, 376C, 377D-377H, %377Dc 377E 377F 377G 377H 377Xc, 377Xf, 386E, 386F, 386H\vfour{, 465R, 495Yb, 495Yc\vfive{, - 556K, 561H}} %4%5 + 556K, 561Hb}} %4%5 }%3 \vtwo{----- {\it see also} $\eusm L^1$, $L^1_{\Bbb C}$, $\|\,\|_1$ @@ -15580,8 +15698,8 @@ \vtwo{$\eusm L^2$ (in $\eusm L^2(\mu)$) 253Yj, \S286\vfour{, 465E, 465F}; %4 - (in $\eusm L^2_{\Bbb C}(\mu)$) 284N, 284O, 284Wh, 284Wi, 284Xi, -284Xk-284Xm, %284Xk 284Xl 284Xm + (in $\eusm L^2_{\Bbb C}(\mu)$) 284N, 284O, 284Wh, 284Wi, 284Xj, +284Xl-284Xn, %284Xl 284Xm 284Xn 284Yg; {\it see also} $L^2$, $\eusm L^p$, $\|\,\|_2$ }%2 @@ -15595,7 +15713,7 @@ 445R, 445S, 445Xm, 445Xn}\vthree{; (in $L^2(\frak A,\bar\mu)$) 366K-366M, %366K 366L 366M 366Xh, 372Qa, 396Ac, 396Xb\vfive{, - 525R}; %5 + 525Q}; %5 (in $L^2_{\Bbb C}(\frak A,\bar\mu)$) {\bf 366M}\vfour{, 494D, 494Xj, 494Xk};}%4%3 {\it see also} $\eusm L^2$, $L^p$, $\|\,\|_2$ @@ -15605,7 +15723,7 @@ \vtwo{$\eusm L^p$ (in $\eusm L^p(\mu)$) {\bf 244A}, 244Da, 244Eb, 244Pa, 244Xa, 244Ya, 244Yi, 246Xg, 252Yh, 253Xh, 255K, {\it 255Of}, 255Ye, 255Yf, 255Yk, 255Yl, -261Xa, 263Xa, 273M, 273Nb, 281Xd, 282Yc, 284Xj, 286A\vfour{, +261Xa, 263Xa, 273M, 273Nb, 281Xd, 282Yc, 284Xk, 286A\vfour{, 411Gh, 412Xd, 415Pa, 415Yj, 415Yk, 416I, 443G, 444R-444U, %444R 444S 444T 444U 444Xt, 444Yi, 444Yo, 472F, 473Ef\vfive{, @@ -15616,7 +15734,7 @@ \vtwo{$L^p$ (in $L^p(\mu)$, $1< p<\infty$) \S244 ({\bf 244A}), 245G, 245Xk, 245Xl, 245Yg, 246Xh, 247Ya, 253Xe, 253Xi, 253Yk, 255Yh\vthree{, 354Xa, 354Yl, 366B, 376N\vfour{, - {\it 411Xe}, 418Yj, 441Kc, 442Xg, 443A, 443G, 443Xh, 443Yu, 444M\vfive{, + {\it 411Xe}, 418Yj, 441Kc, 442Xg, 443A, 443G, 443Xh, 443Yf, 444M\vfive{, 529Xa, 538Kb, 564Xc}}}; %4%3%5 \vthree{(in $L^p(\frak A,\bar\mu)=L^p_{\bar\mu}$, $1< p<\infty$) {\bf 366A}, 366B-366E, %366B 366C 366D 366E @@ -15625,7 +15743,7 @@ 366Xe, 366Xi-366Xk, %366Xi 366Xj 366Xk 366Yf, 366Yi, 369L, 371Gd, 372Xs, 372Yb, 373Bb, 373F, 376Xb\vfour{, - 443Yu\vfive{, + 443Yf\vfive{, 529Ba, 566Xe}}; }%3%4%5 \vthree{ (in $L^p_{\Bbb C}(\mu)$, $1< p<\infty$) 354Yl\vfour{, 443Xz}; }%3%4 @@ -15662,7 +15780,7 @@ \vthree{----- (in $L^{\infty}(\frak A)$) \S363 ({\bf 363A}), 364J, 364Xh, 365L, 365M, 365N, {\it 365Xk}, 367Nc, 368Qa, 372Yq, 377A, 395N\vfour{, - 436Xp, 437B, 437J, 443Ad, 443Jb, 443Yt, 447Yb, 457A\vfive{, + 436Xp, 437B, 437J, 443Ad, 443Jb, 443Ye, 447Yb, 457A\vfive{, 515Mb, {\it 566Ad}, 566Xf}} %3%4%5 }%3 @@ -15814,7 +15932,7 @@ ({\bf 464I}) }%4 -\vfour{$M_r$ (space of $r\times r$ matrices) 446A +\vfour{$M_r$ (space of $r\times r$ matrices) 446Aa }%4 \vfour{$M_t$ (space of signed tight Borel measures) 437Fb, {\bf 437G}, @@ -15870,7 +15988,7 @@ \vfive{$\frakmctbl$ {\bf 517O}, 517P, 517Q, 522B, 522E, 522G, 522I, 522J, 522R-522V, %522R {\it 522S} 522Td 522Uf 522Vb 522Ye-522Yf, %522Ye 522Yf -525Q, 526Xc, 529Xg, 534Bc, 534I, 536Cg, 539Ga, 539H, 553Yc, +525P, 526Xc, 529Xg, 534Bc, 534I, 536Dh, 539Ga, 539H, 553Yc, 554Da, 554F, 555L; {\it see also} axiom }%5 @@ -15900,8 +16018,9 @@ \vfive{$\MahcrR$ ({\it in} $\MahcrR(X)$) {\bf 532A}, 532B, 532C, 532G, 532I-532L, %532I 532J 532K 532L -532P, 532Q, 532R, 532S, 532Xa-532Xc, %532Xa 532Xb 532Xc -532Xd, 532Ya, 532Zb +532P-532S, %532P 532Q 532R 532S +532Xa-532Xd, %532Xa 532Xb 532Xc 532Xd +532Ya, 532Zb }%5 \vfive{$\MahqR$ ({\it in} $\MahqR(X)$) {\bf 531Xe}, 531Ya @@ -15925,7 +16044,7 @@ \indexmedskip%$N \indexheader{$\scriptstyle\pmb{N}$} -\vtwo{$\Bbb N$\vthree{ 3A1H\vfive{, 511Xi}; } +\vtwo{$\Bbb N$\vthree{ 3A1H\vfive{, 511Xk}; } {\it see\vthree{ also}} power set }%2 @@ -15944,7 +16063,7 @@ {\it 421H-421K}, %{\it 421H}{\it 421I}{\it 421J}{\it 421K} {\it 421M}, {\it 421Xe}, {\it 421Xn}, {\it 422Dh}, 422F, {\it 431D}, 434Yp, 4A3Fb\vfive{, - 522Vb, 561Xd, 5A4J}%5 + 522Vb, 561Xe, 5A4I}%5 }%4 \vfive{$\Cal N$ {\it see} null ideal @@ -15957,7 +16076,7 @@ }%5 \vfive{$\non$ (in $\non(X,\Cal I)$, $\non\Cal I$) {\it see} -uniformity ({\bf 511Fa}) +uniformity ({\bf 511Fb}) }%5 \vfive{$\nw$ (in $\nw(X)$) see network weight ({\bf 5A4Ai}) @@ -15981,7 +16100,7 @@ \vfive{$\frak p=\frak m_{\sigma\text{-centered}}$ {\bf 517O}, 517R, 517Xk, 517Yc, {\it 522S}, 522Tc, 522Ua, 522Ye, 526Yb, 526Yf, -535Yd, 539Xb, 544Na, 553Ye, 555K; +535Yd, 536C, 539Xb, 544Na, 553Ye, 555K; {\it see also} axiom }%5 @@ -16041,7 +16160,7 @@ $\Bbb Q$ (the set of rational numbers) 111Eb, 1A1Ef\vthree{, 364Yh\vfour{, 439S, 442Xc\vfive{, - 511Xi, 518Xd}; %5 + 511Xk, 518Xd}; %5 (as topological group) 445Xa }%4 }%3 @@ -16060,7 +16179,7 @@ 2A1Ha, 2A1Lb\vthree{, 352M\vfour{, 4A1Ac, 4A2Gf, 4A2Ua\vfive{, - 511Xi, 518Xd, 561Xc, 5A3Qb}; %5 + 511Xk, 518Xd, 561Xc, 5A3Qb}; %5 (as topological group) 442Xc, 445Ba, 445Xa, 445Xk\vfive{; (in forcing languages) 5A3L, 5A3M}}}}%4%3%2%5 %BbbR @@ -16087,7 +16206,7 @@ \vfour{$r$ (in $r(u)$, where $u$ is in a Banach algebra) {\it see} spectral radius ({\bf 4A6G}); (in $r(T)$, where $T$ is a tree) {\it see} rank -({\bf 421N}\vfive{, {\bf 562Ab}}) +({\bf 421N}\vfive{, {\bf 562Ac}}) }%4 \vfive{$\frak r$ (in $\frak r(\theta,\lambda)$) {\it see} reaping number @@ -16164,18 +16283,19 @@ $\sat^{\downarrow}(P)$) {\it see} saturation ({\bf 511B}) }%5 -\vtwo{$_{sf}$ (in $\mu_{sf}$) {\it see} semi-finite version of a measure ({\bf 213Xc}); - (in $\mu^*_{sf}$) {\bf 213Xf}, 213Xg, 213Xk +\vtwo{$_{\text{sf}}$ (in $\mu_{\text{sf}}$) +{\it see} semi-finite version of a measure ({\bf 213Xc}); + (in $\mu^*_{\text{sf}}$) {\bf 213Xg}, 213Xi }%2 %$\sgn$ {\bf 244F} \vfive{$\shr$ (in $\shr(X,\Cal I)$, $\shr\Cal I$) {\it see} -shrinking number ({\bf 511Fb}) +shrinking number ({\bf 511Fc}) }%5 \vfive{$\shr^+$ (in $\shr^+(X,\Cal I)$, $\shr^+\Cal I$) {\it see} -augmented shrinking number ({\bf 511Fb}) +augmented shrinking number ({\bf 511Fc}) }%5 \vfive{$\CalSmz$ (in $\CalSmz(X,\Cal W)$ or $\CalSmz(X,\rho)$) {\it see} @@ -16201,12 +16321,12 @@ }%5 \vfour{T$_0$ topology 437Xq, 437Xv, {\bf 4A2A}, 4A3Gb\vfive{, - 514Xg, {\it 552Oa}}%5 + 514Xg, {\it 552Oa}, 562Ya}%5 }%4 \vthree{T$_1$ topology {\bf 3A3Aa}, 393J, 393Q\vfour{, 437Rc, {\it 437Xq}, 495Xd, {\bf 4A2A}, 4A2F, 4A2Tb\vfive{, - 561Xd}}%4%5 + 561Xe}}%4%5 }%3 \vfive{$\Cal T$ (the set of well-capped trees) {\bf 562A} @@ -16275,7 +16395,7 @@ \vfive{$\CalUn$ {\it see} universally negligible set ({\bf 439B}) }%5 544La -%\vfive{unif (in unif($\Cal I)$) {\it see} uniformity ({\bf 511Fa}) +%\vfive{unif (in unif($\Cal I)$) {\it see} uniformity ({\bf 511Fb}) %}%5 \vthree{$\upr$ (in $\upr(a,\frak C)$) {\it see} upper envelope ({\bf 313S}) @@ -16286,7 +16406,7 @@ \vfour{usco-compact relation {\bf 422A}, 422B-422G, %422B 422C 422D 422E {\it 422F} 422G -422Xa, 432Xh, 432Yb, 443Yp, 467Ha\vfive{, +422Xa, 432Xh, 432Yb, 443Yr, 467Ha\vfive{, 513Nb, 5A4Db}%5 }%4 @@ -16349,7 +16469,8 @@ \vtwo{\indexmedskip\indexheader{$\scriptstyle\pmb{\beta}$}} %beta -\vtwo{$\beta_r$ (volume of unit ball in $\BbbR^r$) 252Q, 252Xi, {\it 265F}, {\it 265H}, {\it 265Xa}, {\it 265Xb}, {\it 265Xe}\vfour{, +\vtwo{$\beta_r$ (volume of unit ball in $\BbbR^r$) 252Q, 252Xi, +{\it 265F}, {\it 265H}, {\it 265Xa}, {\it 265Xb}, {\it 265Xe}\vfour{, {\it 474S}}%4 }%2 @@ -16423,25 +16544,39 @@ \indexmedskip%pi \indexheader{$\scriptstyle\pmb{\pi}$} -\vfive{$\pi$ (in $\pi(\frak A)$, $\pi(X)$) {\it see} $\pi$-weight -({\bf 511Dc}, {\bf 5A4Ab}) +\vfive{$\pi$ (in $\pi(\frak A)$, $\pi(\mu)$, $\pi(X)$) +{\it see} $\pi$-weight +({\bf 511Dc}, {\bf 511Gb}, {\bf 5A4Ab}) }%5 \vfour{$\pi$-base for a topology 411Ng, {\bf 4A2A}, 4A2G\vfive{, 514S, 535La, 561Eb, 561Yd, 561Ye, 5A4Ab}%5 }%4 -\vfive{$\pi$-weight (of a Boolean algebra) {\bf 511Dc}, 511I, 512Ec, 514Bc, -514Da, 514E, 514Hb, 514Ja, -514Nb, 514Xb, 514Xc, 514Yb, 514Yd, -516Lb, 516Xb, 521Xl, 523Ya, 524Mc, 524Xb, 527Db, 527N, 527Yc, +\vfive{$\pi$-weight (of a Boolean algebra) 4A3S, +{\bf 511Dc}, 511I, 512Ec, 514Bc, 514Da, 514E, 514Hb, 514Ja, +514Nb, 514Xb, 514Xc, 514Yb, 514Yd, 516Lb, 516Xb, 517P, 523Ya, +527Db, 527N, 527Xg, 527Yc, 528Pb, 528Qa, 528Xg, 528Ye, 529Ye, 546Ha, 546Ld, 546M, 546Xb, -546Yb, 546Zd, 547H, 554A, 555Za; - (of a topological space) 512Eb, 512Xg, 514Bc, 514Hb, -514Ja, 514Nb, 516Nb, 546E, {\bf 5A4Ab}, 5A4Ba; - {\it see also} countable $\pi$-weight +546Yb, 546Zd, 554A, 555Za +}%5 + +\vfive{----- (of a measure) 463Yd, {\bf 511Gb}, +511Xd-511Xg, %511Xd, 511Xe, 511Xf 511Xg, +521Xc, 521Xl-521Xo, %521Xl, 521Xm, 521Xn, 521Xo +{\it 522 notes}, 524P, 524Qb, 524Ub, 536C, 536Dg, 547Xd +}%5 + +\vfive{----- (of a measure algebra) 521Xl, +524Mc, 524P, 524Qb, 524Ub, 524Xb, 528Pb, 528Xg, 547H +}%5 + +\vfive{----- (of a topological space) 512Eb, 512Xg, 514Bc, 514Hb, +514Ja, 514Nb, 516Nb, 517Pc, 522Yi, 526Xd, 527J, 546E, {\bf 5A4Ab}, 5A4Ba }%5 +%the above include "countable $\pi$-weight" + $\pi$-$\lambda$ Theorem {\it see} Monotone Class Theorem (136B) \indexmedskip%pi @@ -16494,7 +16629,7 @@ 526Ya, 534Fd}%5 }%4 -\vfour{----- locally compact group 443Q, 443Xl, 443Yh, 443Yn, +\vfour{----- locally compact group 443Q, 443Xl, 443Yi, 443Yo, {\it 447E-447G}, %{\it 447E}{\it 447F}{\it 447G} 448T, 4A5El, 4A5S\vfive{, {\it 531Xf}, 534H}%5 @@ -16520,7 +16655,7 @@ \vthree{$\sigma$-finite measure algebra {\bf 322Ac}, 322Bc, 322C, 322G, {\it 322N}, 323Gb, {\it 323Ya}, 324K, 325Eb, 327Be, 331N, 331Xk, 362Xd, 367Md, 367P, 367Xq, 367Xs, 369Xg, 383E, 393Xi\vfour{, - 437Yv, 448Xj, 494Be, 494C, 494Xg, 494Yi\vfive{, + 437Yv, 448Xi, 494Be, 494C, 494Xg, 494Yi\vfive{, 528K, 528N, 528Xf, 566Md}}%4%5 }%3 sigma-finite m alg @@ -16542,9 +16677,9 @@ {\it 444Xm}, {\it 452I}, {\it 441Xe}, {\it 441Xh}, 443Xl, 448Q-448T, %448Q 448R 448S 448T {\it 451Pc}, 451Xn, -463Cd, 463G, 463H, 463K, 463L, 463Xb, 463Xc, 463Xe, 463Xj, 463Yd, +463Cd, 463G, 463H, 463K, 463L, 463Xb, 436Xd, 436Xf, 463Xk, 463Yd, {\it 465Xe}, 491Ys, 495H, 495I, 495Nc, 495Xb\vfive{, - 522Va, {\it 524B}, {\it 524Fb}, 524Pf, {\it 524R}, + 522Va, {\it 524B}, {\it 524Fb}, 524Qf, {\it 524S}, {\it 527O}, 535Eb, 535I, 535P, 535Xl, 535Yc, {\it 537Bb}, {\it 543C}, 566E; {\it see also} codably $\sigma$-finite ({\bf 563Ad})}}}%5%4%3 }%2 \sigma-finite measure @@ -16576,7 +16711,7 @@ \indexheader{$\sigma$-isolated} \vfour{$\sigma$-isolated family of sets 438K, 438Ld, {\it 438N}, 438Xn, -466D, 466Eb, 466Ye, 467Pb, 467Ye, {\bf 4A2A} +466D, 466Eb, 466Yb, 467Pb, 467Ye, {\bf 4A2A} }%4 \indexheader{$\sigma$-linked} @@ -16640,7 +16775,7 @@ \indexheader{$\scriptstyle\pmb{\Sigma}$} \vfour{$\pmb{\Sigma}^1_n$ set in a Polish space {\bf 423Ra}; -{\it see also} PCA ({\bf 432R}) +{\it see also} PCA ({\bf 423R}) }%4 \vfour{$\Sigma_{\text{um}}$ (algebra of universally measurable sets) @@ -16679,7 +16814,7 @@ 436Xg, 436Xj, 437Kc, 437Yh, 439Xh, 444Yb, 451Xo, 452C, 453Dc, 453H, 454Sb, 456N, 456O, 461F, {\it 462Yc}, 465S, 465T, 465Xj, {\it 466H}, 466Xc, -{\it 466Xm}, 476B, 481N, 482Xd, 491Ce\vfive{, +{\it 466Xr}, 476B, 481N, 482Xd, 491Ce\vfive{, 531Yc, 532D, 532E, 532Xf, {\it 533Xi}, 535H, 563Bc}; %5 {\it see also} quasi-Radon measure ({\bf 411Ha}), signed $\tau$-additive measure ({\bf 437G}), $M_{\tau}$ @@ -16764,10 +16899,10 @@ 419F, 419G, 419Yb, 421P, 435Xb, 435Xi, 435Xk, {\it 438C}, 439Xp, 463Xh, 463Yd, 463Ye, 4A1A, 4A1Bb, 4A1Eb, 4A1M, 4A1N\vfive{, - {\it 515Ya}, 521K, {\it 522B}, {\it 522F}, 522T, 525Hc, 525Ud, 525Xb, + {\it 515Ya}, 521K, {\it 522B}, {\it 522F}, 522T, 525Gc, 525Td, 525Xb, {\it 529H}, 535Ya, -536C, 533E, 533H, 539P, 546Ya, 546Zc, 546Zd, 547Za, 553F, 556Xb, -561A, 561Xr, 561Ya, 561Yb, 562Ac, 567Ed, +536D, 533E, 533H, 539P, 546Ya, 546Zc, 546Zd, 547Za, 553F, 556Xb, +561A, 561Xd, 561Ya, 561Yb, 562Ac, 567Ed, 567L, 567Xd, 567Xm, 567Xn}; %5 {\it see also} \vfive{axiom,} continuum hypothesis, power set}%4 }%2 \omega_1 @@ -16946,8 +17081,8 @@ *\vtwo{ (in weak*) {\it see} weak* topology ({\bf 2A5Ig}\vfour{, {\bf 4A4Bd}}); }%2%4 -\vtwo{ (in $U^*=\eurm B(U;\Bbb R)$, linear topological space dual) {\it see} dual -({\bf 2A4H}\vfour{, {\bf 4A4Bd}}); } %2 +\vtwo{ (in $U^*=\eurm B(U;\Bbb R)$, linear topological space dual) +{\it see} dual ({\bf 2A4H}\vfour{, {\bf 4A4Bd}}); } %2 \vthree{ (in $u^*$) {\it see} decreasing rearrangement ({\bf 373C}); } %3 (in $\mu^*$) {\it see} outer measure defined by a measure ({\bf 132B}) @@ -16974,10 +17109,8 @@ smooth dual ({\bf 437Ab}) }%4 -\vfour{$\ssptilde$ (in $\tilde a$, $\tilde f$, $\tilde u$) -{\bf 443Af}, 443Xe, 443Xh, 444R, 444Vc, 444Xu\vfive{; - (in $\tilde H$) 551K, 551L}%5 -}%4 +\vfive{$\ssptilde$ (in $\tilde H$) 551K, 551L +}%5 \vthree{$^{\times}$ (in $U^{\times}$) {\it see} order-continuous dual ({\bf 356A}); (in $U^{\times\times}$) {\it see} order-continuous bidual }%3 @@ -17040,7 +17173,8 @@ }%2 \vtwo{$\|\,\|_p$ (for $1