added fact from exercise sheet

2023-07-19 23:54:55 +02:00 · 2023-07-19 23:54:55 +02:00 · 1ff341e106
commit 1ff341e106
parent ee6d9c917d
1 changed files with 5 additions and 0 deletions
--- a/inputs/lecture_08.tex
+++ b/inputs/lecture_08.tex
@ -146,3 +146,8 @@ for any $k \in \N$.
    \]
    hence $\bP[T] \in \{0,1\}$.
 \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}