Added existence of the Haar measure.

src/measure/lcg/lcg.tex

@@ -6,4 +6,10 @@
     Let $G$ be a topological group, then $G$ is \textbf{locally compact} if $G$ is a LCH space. 
 \end{definition}
 
-
+\begin{proposition}
+\label{proposition:lcg-cc-uc}
+    Let $G$ be a locally compact group, $E$ be a TVS over $K \in \RC$, and $\phi \in C_c(G; E)$, then $\phi$ is left and right uniformly continuous. 
+\end{proposition}
+\begin{proof}
+    By \autoref{lemma:lch-compact-neighbour}, there exists a compact neighbourhood $U \in \cn_G(\text{supp}(\phi))$. By \autoref{proposition:uniform-continuous-compact}, $\phi|_{U}$ and $\phi|_{\supp(\phi)^c}$ are both left and right uniformly continuous. Therefore $\phi$ is left and right uniformly continuous. 
+\end{proof}