added fact from exercise sheet

This commit is contained in:
Josia Pietsch 2023-07-19 23:54:55 +02:00
parent ee6d9c917d
commit 1ff341e106
Signed by: jrpie
GPG key ID: E70B571D66986A2D

View file

@ -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}