jrpie-notes/probability-theory
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Josia Pietsch 2023-07-17 19:57:26 +02:00
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inputs/lecture_17.tex
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@ -174,7 +174,7 @@ Let
We have We have
\begin{IEEEeqnarray*}{rCl} \begin{IEEEeqnarray*}{rCl}
\Lambda &=& \{\omega | \liminf_N X_N(\omega) < \limsup_N X_N(\omega)\}\\ \Lambda &=& \{\omega | \liminf_N X_N(\omega) < \limsup_N X_N(\omega)\}\\
&=& \{\omega | \liminf_N X_N(\omega) < a < b \limsup_N X_N(\omega)\} \\ &=& \{\omega | \liminf_N X_N(\omega) < a < b < \limsup_N X_N(\omega)\} \\
&=& \bigcup_{a,b \in \Q} \underbrace{\{\omega | \liminf_N X_N(\omega) < a < b < \limsup_N X_N(\omega)\}}_{\Lambda_{a,b}} \\ &=& \bigcup_{a,b \in \Q} \underbrace{\{\omega | \liminf_N X_N(\omega) < a < b < \limsup_N X_N(\omega)\}}_{\Lambda_{a,b}} \\
\end{IEEEeqnarray*} \end{IEEEeqnarray*}