From ee6f4fe8515d571eba454896eb09b5aa2da02b45 Mon Sep 17 00:00:00 2001
From: Josia Pietsch <git@jrpie.de>
Date: Fri, 19 May 2023 13:44:26 +0200
Subject: [PATCH] fixed remark regarding tail sigma algebra

---
 inputs/lecture_8.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/inputs/lecture_8.tex b/inputs/lecture_8.tex
index f504009..7b67105 100644
--- a/inputs/lecture_8.tex
+++ b/inputs/lecture_8.tex
@@ -24,7 +24,7 @@ of sequences of random variables.
             is again a $\sigma$-algebra, $\cT$ is indeed a $\sigma$-algebra.
         \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{remark}