Adjusted citation formats. Moved citation off of named theorems if possible.

src/measure/lebesgue-integral/non-negative.tex

@@ -38,7 +38,7 @@
     the two sides are equal.
 \end{proof}
 
-\begin{theorem}[Monotone Convergence Theorem, {{\cite[Theorem 2.14]{Folland}}}]
+\begin{theorem}[Monotone Convergence Theorem]
 \label{theorem:mct}
     Let $(X, \cm, \mu)$ be a measure space, $\seq{f_n} \subset \mathcal{L}^+(X, \cm)$, and $f \in \mathcal{L}^+(X, \cm)$ such that $f_n \upto f$ pointwise, then
     \[
@@ -46,7 +46,7 @@
     \]
 
 \end{theorem}
-\begin{proof}
+\begin{proof}[Proof {{\cite[Theorem 2.14]{Folland}}}. ]
     By \autoref{definition:lebesgue-non-negative}, $\int f_n d\mu \le \int f d\mu$ for each $n \in \natp$.
 
     Let $\phi \in \Sigma^+(X, \cm)$ with $\phi|_{\bracs{f > 0}} < f|_{\bracs{f > 0}}$ and $\phi \le f$. Since $f_n \upto f$, $\bracs{f_n \ge \phi} \upto X$. In which case, since $A \mapsto \int \one_A \phi d\mu$ is a measure (\autoref{proposition:lebesgue-simple-properties}),
@@ -57,7 +57,7 @@
     by continuity from below (\autoref{proposition:measure-properties}). Therefore $\limv{n}\int f_n d\mu \ge \int f$ by \autoref{lemma:lebesgue-non-negative-strict}.
 \end{proof}
 
-\begin{lemma}[Fatou, {{\cite[Lemma 2.18]{Folland}}}]
+\begin{lemma}[Fatou]
 \label{lemma:fatou}
     Let $(X, \cm, \mu)$ be a measure space, $\seq{f_n} \subset \mathcal{L}^+(X, \cm)$, then
     \[
@@ -65,7 +65,7 @@
     \]
 
 \end{lemma}
-\begin{proof}
+\begin{proof}[Proof {{\cite[Lemma 2.18]{Folland}}}. ]
     For each $n \in \natp$, $\inf_{k \ge n}f_k \le f_n$. By the monotone convergence theorem,
     \[
     \int \liminf_{n \to \infty}f_n d\mu = \limv{n}\int \inf_{k \ge n}f_k d\mu