Minor adjustment.

src/measure/measure/localisable.tex

@@ -182,9 +182,9 @@
         \item For each $A \in \cf$, $f_n|_A = f_{A, n}$ almost everywhere. 
     \end{enumerate}
     
-    Since $Y$ is Polish, \autoref{proposition:metric-measurable-limit} implies that $\bracsn{\limv{n}f_n \text{ exists}} \in \cm$. For each $A \in \cf$, since $\limv{n}f_{A, n}$ and $\limv{n}f_{n}|_A$ exist and are equal almost everywhere on $A$, 
+    Since $Y$ is Polish, \autoref{proposition:metric-measurable-limit} implies that $\bracsn{\limv{n}f_n \text{ exists}} \in \cm$. For each $A \in \cf$, since $f_n|_A = f_{A, n}$ almost everywhere, $\limv{n}f_{A, n}$ and $\limv{n}f_{n}|_A$ exist and are equal almost everywhere on $A$. Thus
     \[
-    \mu\paren{\bracs{\limv{n}f_n \text{ does not exist}} \cap A} \le \mu\bracs{\limv{n}f_{A, n} \text{ does not exist}} = 0
+    \mu\paren{\bracs{\limv{n}f_n \text{ does not exist}} \cap A} \le \mu\bracs{\limv{n}f_{A, n} \text{ does not exist}} + 0 = 0
     \]
 
     As $\mu$ is semifinite, $\mu\bracsn{\limv{n}f_n \text{ does not exist}} = 0$, so there exists $f \in \mathcal{L}^0(X; Y)$ such that $f = \limv{n}f_n$ almost everywhere. In which case,