diff --git a/inputs/lecture_09.tex b/inputs/lecture_09.tex
index c07f0b4..e27f18f 100644
--- a/inputs/lecture_09.tex
+++ b/inputs/lecture_09.tex
@@ -94,9 +94,8 @@ characteristic functions of Fourier transforms.
    with Lebesgue density
    \[
    f_{\mu \ast \nu}(x) \coloneqq
-       \int_{\R^d} f_\mu(x - t) f\nu(t) \lambda^d(\dif t)
-   \] 
-    
+       \int_{\R^d} f_\mu(x - t) f_\nu(t) \lambda^d(\dif t).
+   \]
 \end{definition}
 
 \begin{fact}+[Exercise 6.1]
@@ -107,7 +106,7 @@ characteristic functions of Fourier transforms.
     has distribution
     \[
     \mu_1 \ast \mu_2 \ast \ldots \ast \mu_n.
-    \] 
+    \]
 \end{fact}
 \todo{TODO}