Added citations for elements taken from Cohn's Measure Theory.

refs.bib

@@ -236,3 +236,15 @@
   doi       = {10.1007/978-1-4471-4820-3},
   isbn      = {978-1-4471-4820-3}
 }
+
+@book{CohnMeasure,
+  author    = {Cohn, Donald L.},
+  title     = {Measure Theory},
+  edition   = {2nd},
+  series    = {Birkhäuser Advanced Texts Basler Lehrbücher},
+  publisher = {Birkhäuser},
+  address   = {New York},
+  year      = {2013},
+  isbn      = {978-1-4614-6955-1},
+  doi       = {10.1007/978-1-4614-6956-8}
+}

src/measure/measurable-maps/metric.tex

@@ -40,7 +40,7 @@
         \item For each $\phi \in C(X; [0, 1])$, $\phi \circ f$ is $(\cm, \cb_\real)$-measurable.
     \end{enumerate}
 \end{proposition}
-\begin{proof}
+\begin{proof}[Proof, {{\cite[Lemma 8.1.9]{CohnMeasure}}}. ]
     (2) $\Rightarrow$ (1): For each $U \subset X$ open, the function
     \[
     d_{U^c}: X \to [0, 1] \quad x \mapsto d(x, U^c) \wedge 1
@@ -57,7 +57,7 @@
         \item If $f = \limv{n}f_n$ exists, then it is $(\cm, \cb_Y)$-measurable.
     \end{enumerate}
 \end{proposition}
-\begin{proof}
+\begin{proof}[Proof, {{\cite[Proposition 8.1.10-8.1.11]{CohnMeasure}}}. ]
     (1): Let $d$ be a complete metric on $Y$, then for any $x \in X$, $\limv{n}f_n(x)$ exists if and only if $\seq{f_n(x)}$ is Cauchy. In which case,
     \[
     \bracs{\limv{n}f_n \text{ exists}} = \bigcap_{k \in \natp}\bigcup_{N \in \natp}\bigcap_{m \in \natp}\bigcap_{n \in \natp}\bracsn{d(f_m, f_n) < 1/k}