From 5e9da4cef17d30bd27999019f446ef8a62d66e1b Mon Sep 17 00:00:00 2001
From: Josia Pietsch <git@jrpie.de>
Date: Thu, 20 Jul 2023 14:02:11 +0200
Subject: [PATCH] fixed typo in orthogonal projection lemma

---
 inputs/lecture_14.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/inputs/lecture_14.tex b/inputs/lecture_14.tex
index dfe485b..91095a3 100644
--- a/inputs/lecture_14.tex
+++ b/inputs/lecture_14.tex
@@ -101,7 +101,7 @@ and then do the harder proof.
     i.e.~$H$ is a vector space with an inner product $\langle \cdot, \cdot \rangle_H$ which defines a norm by $\|x\|_H^2 = \langle x, x\rangle_H$
     making $H$ a complete metric space.
 
-    For any $x \in H$ and $K \subseteq H$ closed and convex,
+    For any $x \in H$ and closed, convex subspace $K \subseteq H$,
     there exists a unique $z \in K$ such that the following equivalent conditions hold:
     \begin{enumerate}[(a)]
         \item  $\forall  y \in K : \langle x-z, y\rangle_H = 0$,