Adjusted notation for spaces of measurable functions.

src/measure/measurable-maps/measurable-maps.tex

@@ -4,10 +4,16 @@
 \begin{definition}[Measurable Function]
 \label{definition:measurable-function}
     Let $(X, \cm)$ and $(Y, \cn)$ be measurable spaces and $f: X \to Y$ be a mapping, then $f$ is \textbf{$(\cm, \cn)$-measurable} if $f^{-1}(E) \in \cm$ for all $E \in \cn$.
-
-    The set $\mathscr{M}(X; Y)$ is the \textbf{space of measurable functions} from $X$ to $Y$. 
 \end{definition}
 
+\begin{definition}[Space of Measurable Functions]
+\label{definition:measurable-function-space}
+    Let $(X, \cm)$ and $(Y, \cn)$ be measurable spaces, then the set $\mathscr{L}^0(X, \cm; Y) = \mathcal{L}^0(X; Y)$ is the \textbf{space of measurable functions} from $X$ to $Y$. 
+
+    For any measure $\mu$ on $(X, \cm)$, the space $L^0(X, \cm, \mu; Y) = L^0(X; Y)$ is the space of measurable functions from $X$ to $Y$, modulo almost everywhere equality. 
+\end{definition}
+
+
 
 \begin{definition}[Borel Measurable]
 \label{definition:borel-measurable-function}