From 5691d2c553822542fcc68ce23e84609b62a718f8 Mon Sep 17 00:00:00 2001
From: Josia Pietsch <josia.pietsch@uni-bonn.de>
Date: Sat, 15 Jul 2023 23:31:10 +0200
Subject: [PATCH] made fact from lecture 13 (somewhat) less trivial

---
 inputs/lecture_13.tex | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/inputs/lecture_13.tex b/inputs/lecture_13.tex
index f4d9d1d..3363e22 100644
--- a/inputs/lecture_13.tex
+++ b/inputs/lecture_13.tex
@@ -274,7 +274,8 @@ We have shown, that $\mu_{n_k} \implies \mu$ along a subsequence.
 We still need to show that $\mu_n \implies \mu$.
 \begin{fact}
     Suppose $a_n$ is a bounded sequence in $\R$,
-    such that any subsequence converges to $a \in \R$.
+    such that any subsequence has a subsequence
+    that converges to $a \in \R$.
     Then $a_n \to  a$.
 \end{fact}
 \begin{subproof}