diff --git a/inputs/lecture_15.tex b/inputs/lecture_15.tex
index 0eaf742..5bd845d 100644
--- a/inputs/lecture_15.tex
+++ b/inputs/lecture_15.tex
@@ -50,7 +50,7 @@ We want to derive some properties of conditional expectation.
     If $X \ge  0$, then $\bE[X | \cG] \ge 0$ a.s.
 \end{theorem}
 \begin{proof}
-    Let $W $ be a version of $\E[X | \cG]$.
+    Let $W $ be a version of $\bE[X | \cG]$.
     Suppose $\bP[ W < 0] > 0$.
     Then $G \coloneqq  \{W < -\frac{1}{n}\} \in \cG$
     For some $n \in \N$, we have $\bP[G] > 0$.
@@ -88,7 +88,7 @@ We want to derive some properties of conditional expectation.
 
     Take some $G \in \cG$.
     We know by (b) % TODO REF
-    that $\be[Z_n \One_G] = \bE[X_n \One_G]$.
+    that $\bE[Z_n \One_G] = \bE[X_n \One_G]$.
     The LHS increases to  $\bE[Z \One_G]$ by the monotone 
     convergence theorem.
     Again by MCT, $\bE[X_n \One_G]$ increases to