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fixed remark regarding tail sigma algebra

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Josia Pietsch 2023-05-19 13:44:26 +02:00
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inputs/lecture_8.tex
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@ -24,7 +24,7 @@ of sequences of random variables.
is again a $\sigma$-algebra, $\cT$ is indeed a $\sigma$-algebra. is again a $\sigma$-algebra, $\cT$ is indeed a $\sigma$-algebra.
\item We have \item We have
\[ \[
\cT = \{A \in \cF ~|~ \forall i \exists B \in \cF^{\otimes \N} : A = \{\omega | (X_i(\omega), X_{i+1}(\omega), \ldots) \in B\} \}. % TODO? \cT = \{A \in \cF ~|~ \forall i ~ \exists B \in \cB(\R)^{\otimes \N} : A = \{\omega | (X_i(\omega), X_{i+1}(\omega), \ldots) \in B\} \}. % TODO?
\] \]
\end{enumerate} \end{enumerate}
\end{remark} \end{remark}