\relax \providecommand\zref@newlabel[2]{} \providecommand\hyper@newdestlabel[2]{} \@writefile{toc}{\contentsline {section}{\numberline {1}Lecture 1 -- Measures and sigma-Fields}{4}{section.1}\protected@file@percent } \newlabel{sec:lec01}{{1}{4}{Lecture 1 -- Measures and sigma-Fields}{section.1}{}} \newlabel{sec:lec01@cref}{{[section][1][]1}{[1][4][]4}{}{}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Notation and set-theoretic preliminaries}{4}{subsection.1.1}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}$\sigma $-fields}{4}{subsection.1.2}\protected@file@percent } \newlabel{def:sigma-field}{{1.1}{4}{$\sigma $-field}{tcb@cnt@definition.1.1}{}} \newlabel{def:sigma-field@cref}{{[tcb@cnt@definition][1][1]1.1}{[1][4][]4}{}{}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Measures}{5}{subsection.1.3}\protected@file@percent } \newlabel{def:measure}{{1.2}{5}{Measure}{tcb@cnt@definition.1.2}{}} \newlabel{def:measure@cref}{{[tcb@cnt@definition][2][1]1.2}{[1][5][]5}{}{}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.4}Special classes of measures}{5}{subsection.1.4}\protected@file@percent } \newlabel{def:special-measures}{{1.3}{5}{Probability, finite, and $\sigma $-finite measures}{tcb@cnt@definition.1.3}{}} \newlabel{def:special-measures@cref}{{[tcb@cnt@definition][3][1]1.3}{[1][5][]5}{}{}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.5}Examples on a finite sample space}{6}{subsection.1.5}\protected@file@percent } \@setckpt{lectures/lecture01}{ \setcounter{page}{7} \setcounter{equation}{0} \setcounter{enumi}{2} \setcounter{enumii}{0} \setcounter{enumiii}{0} \setcounter{enumiv}{0} \setcounter{footnote}{0} \setcounter{mpfootnote}{0} \setcounter{part}{0} \setcounter{section}{1} \setcounter{subsection}{5} \setcounter{subsubsection}{0} \setcounter{paragraph}{0} \setcounter{subparagraph}{0} \setcounter{figure}{0} \setcounter{table}{0} \setcounter{parentequation}{0} \setcounter{caption@flags}{0} \setcounter{continuedfloat}{0} \setcounter{section@level}{0} \setcounter{Item}{5} \setcounter{Hfootnote}{0} \setcounter{bookmark@seq@number}{6} \setcounter{tcbbreakpart}{1} \setcounter{tcblayer}{0} \setcounter{tcolorbox@number}{3} \setcounter{tcbrastercolumn}{1} \setcounter{tcbrasterrow}{1} \setcounter{tcbrasternum}{1} \setcounter{tcbraster}{0} \setcounter{lstnumber}{1} \setcounter{tcblisting}{0} \setcounter{tcb@cnt@definition}{3} \setcounter{mdf@globalstyle@cnt}{0} \setcounter{mdfcountframes}{0} \setcounter{mdf@env@i}{0} \setcounter{mdf@env@ii}{0} \setcounter{mdf@zref@counter}{0} \setcounter{example}{3} \setcounter{remark}{5} \setcounter{note}{0} \setcounter{lstlisting}{0} }