\relax 
\providecommand\zref@newlabel[2]{}
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\@writefile{toc}{\contentsline {section}{\numberline {1}Lecture 12 -- Central Limit Theorem; Characteristic Functions}{1}{section.1}\protected@file@percent }
\newlabel{sec:lec12}{{1}{1}{Lecture 12 -- Central Limit Theorem; Characteristic Functions}{section.1}{}}
\newlabel{sec:lec12@cref}{{[section][1][]1}{[1][1][]1}{}{}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Tightness and Prohorov's theorem}{1}{subsection.1.1}\protected@file@percent }
\newlabel{def:uniform-tightness}{{1.1}{1}{Uniform tightness}{tcb@cnt@definition.1.1}{}}
\newlabel{def:uniform-tightness@cref}{{[tcb@cnt@definition][1][1]1.1}{[1][1][]1}{}{}{}}
\newlabel{thm:prohorov}{{1.2}{1}{Prohorov}{tcb@cnt@definition.1.2}{}}
\newlabel{thm:prohorov@cref}{{[tcb@cnt@definition][2][1]1.2}{[1][1][]1}{}{}{}}
\newlabel{prop:subsubseq}{{1.3}{1}{Subsubsequence criterion for weak convergence}{tcb@cnt@definition.1.3}{}}
\newlabel{prop:subsubseq@cref}{{[tcb@cnt@definition][3][1]1.3}{[1][1][]1}{}{}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Gaussian measures}{1}{subsection.1.2}\protected@file@percent }
\newlabel{def:gaussian-r}{{1.4}{1}{Gaussian measure on \texorpdfstring {$\R $}{R}}{tcb@cnt@definition.1.4}{}}
\newlabel{def:gaussian-r@cref}{{[tcb@cnt@definition][4][1]1.4}{[1][1][]1}{}{}{}}
\newlabel{def:gaussian-rd}{{1.5}{2}{Gaussian measure on \texorpdfstring {$\R ^d$}{Rd}}{tcb@cnt@definition.1.5}{}}
\newlabel{def:gaussian-rd@cref}{{[tcb@cnt@definition][5][1]1.5}{[1][1][]2}{}{}{}}
\newlabel{def:gaussian-rv}{{1.6}{2}{Gaussian random variable}{tcb@cnt@definition.1.6}{}}
\newlabel{def:gaussian-rv@cref}{{[tcb@cnt@definition][6][1]1.6}{[1][2][]2}{}{}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Characteristic functions}{2}{subsection.1.3}\protected@file@percent }
\newlabel{def:char-fn}{{1.7}{2}{Characteristic function}{tcb@cnt@definition.1.7}{}}
\newlabel{def:char-fn@cref}{{[tcb@cnt@definition][7][1]1.7}{[1][2][]2}{}{}{}}
\newlabel{def:convolution}{{1.8}{2}{Convolution of measures}{tcb@cnt@definition.1.8}{}}
\newlabel{def:convolution@cref}{{[tcb@cnt@definition][8][1]1.8}{[1][2][]2}{}{}{}}
\newlabel{thm:char-unique}{{1.9}{2}{Uniqueness of characteristic functions}{tcb@cnt@definition.1.9}{}}
\newlabel{thm:char-unique@cref}{{[tcb@cnt@definition][9][1]1.9}{[1][2][]2}{}{}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.4}L\'evy's continuity lemma}{3}{subsection.1.4}\protected@file@percent }
\newlabel{lem:levy-continuity}{{1.10}{3}{L\'evy continuity}{tcb@cnt@definition.1.10}{}}
\newlabel{lem:levy-continuity@cref}{{[tcb@cnt@definition][10][1]1.10}{[1][3][]3}{}{}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.5}The central limit theorem}{3}{subsection.1.5}\protected@file@percent }
\newlabel{thm:clt}{{1.11}{3}{Central limit theorem}{tcb@cnt@definition.1.11}{}}
\newlabel{thm:clt@cref}{{[tcb@cnt@definition][11][1]1.11}{[1][3][]3}{}{}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Architecture of the CLT proof: tightness and pointwise convergence of characteristic functions feed into L\'evy's lemma; the limiting characteristic function identifies the Gaussian \(Z\).}}{4}{figure.caption.1}\protected@file@percent }
\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
\newlabel{fig:clt-architecture}{{1}{4}{Architecture of the CLT proof: tightness and pointwise convergence of characteristic functions feed into L\'evy's lemma; the limiting characteristic function identifies the Gaussian \(Z\)}{figure.caption.1}{}}
\newlabel{fig:clt-architecture@cref}{{[figure][1][]1}{[1][4][]4}{}{}{}}
\gdef \@abspage@last{4}