added fact from exercise sheet

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Josia Pietsch 2023-07-19 23:54:55 +02:00
parent ee6d9c917d
commit 1ff341e106
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@ -146,3 +146,8 @@ for any $k \in \N$.
\] \]
hence $\bP[T] \in \{0,1\}$. hence $\bP[T] \in \{0,1\}$.
\end{refproof} \end{refproof}
\begin{fact}+[Exercise 5.2 (b)]
Any random variable measurable with respect to a $\bP$-trivial
$\sigma$-algebra is a.s.~a constant.
\end{fact}
%\todo{copy proof}