Added the Bochner integral.

src/measure/lebesgue-integral/simple.tex

@@ -8,7 +8,7 @@
 
 \begin{definition}[Integral of Non-Negative Simple Functions]
 \label{definition:lebesgue-simple}
-    Let $(X, \cm, \mu)$ be a measure space and $f = \sum_{y \in f(X)}y \cdot \one_{\bracs{f = y}} \in \Sigma^+(X, \cm)$ be a non-negative simple function in standard form, then\footnote{With the convention that $0 \cdot \infty = 0$.}
+    Let $(X, \cm, \mu)$ be a measure space and $f = \sum_{y \in f(X)}y \cdot \one_{\bracs{f = y}} \in \Sigma^+(X, \cm)$ be a non-negative simple function in standard form, then (with the convention that $0 \cdot \infty = 0$)
     \[
     \int f d\mu = \int f(x) \mu(dx) = \sum_{y \in f(X)}y \cdot \mu(\bracs{f = y})
     \]