From 369308a9f8608cb13d5642f315c720deed67cf31 Mon Sep 17 00:00:00 2001
From: Josia Pietsch <josia.pietsch@uni-bonn.de>
Date: Wed, 12 Jul 2023 15:25:52 +0200
Subject: [PATCH] 09 typos

---
 inputs/lecture_09.tex | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/inputs/lecture_09.tex b/inputs/lecture_09.tex
index 186f033..ddac17e 100644
--- a/inputs/lecture_09.tex
+++ b/inputs/lecture_09.tex
@@ -113,9 +113,11 @@ We have
     $X: (\Omega, \cF) \to  (\R, \cB(\R))$ is a random variable.
     Then we can define
     \[
-    \phi_X(t) \coloneqq  \bE[e^{\i t x}] = \int e^{\i t X(\omega)} \bP(d \omega) = \int_{\R} e^{\i t x} \mu(dx) = \phi_\mu(t)
+    \phi_X(t) \coloneqq  \bE[e^{\i t x}]
+      = \int e^{\i t X(\omega)} \bP(\dif \omega)
+      = \int_{\R} e^{\i t x} \mu(dx) = \phi_\mu(t),
     \]
-    where $\mu = \bP x^{-1}$.
+    where $\mu = \bP \circ X^{-1}$.
 \end{remark}
 
 \begin{theorem}[Inversion formula] % thm1