From c926a076e701b234e88fc2eb6f6adb58e84201fb Mon Sep 17 00:00:00 2001
From: Josia Pietsch <josia.pietsch@uni-bonn.de>
Date: Wed, 12 Jul 2023 17:57:05 +0200
Subject: [PATCH] lecture 12 define g(h)

---
 inputs/lecture_12.tex | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/inputs/lecture_12.tex b/inputs/lecture_12.tex
index 63d95b8..1fa9a32 100644
--- a/inputs/lecture_12.tex
+++ b/inputs/lecture_12.tex
@@ -38,7 +38,8 @@ First, we need to prove some properties of characteristic functions.
                                           &=& |\bE[e^{\i t X} (e^{\i h X} - 1)]|\\
                                           &\overset{\text{Jensen}}{\le}&
                                           \bE[|e^{\i t X}| \cdot  |e^{\i h X} -1|]\\
-                                          &=& \bE[|e^{\i h X} - 1|]\\
+                                          &=& \bE[|e^{\i h X} - 1|]
+                                          \text{\reflectbox{$\coloneqq$}} g(h)\\
             \end{IEEEeqnarray*}
 
             Hence $\sup_{t \in \R} |\phi_X(t + h) - \phi_X(t) | \le  g(h)$.