Fixed typos in the haar proof.

src/measure/lcg/haar.tex

@@ -45,7 +45,7 @@
     Let $G$ be a locally compact group and $f, h, g \in C_c^+(G)$, then:
     \begin{enumerate}
         \item If $g \ne 0$, then $(f: g) < \infty$. 
-        \item $(f, h: g) \le (h: g) + (h: g)$. 
+        \item $(f + h: g) \le (f: g) + (h: g)$. 
         \item For each $\lambda \ge 0$, $(\lambda f: g) = \lambda(f: g)$. 
         \item If $f \le h$, then $(f: g) \le (h: g)$. 
         \item $(f: g) \le (f: h)(h: g)$. 
@@ -126,7 +126,7 @@
         \item For each $f \in C_c^+(G) \setminus \bracs{0}$, $I(f) \in [(h: f)^{-1}, (f: h)]$. 
         \item For every $\lambda \ge 0$ and $f \in C_c^+(G)$, $I(\lambda f) = \lambda I(f)$.
         \item For any $x \in G$, $I(L_xf) = I(f)$. 
-        \item For each $f, f' \in C_c^+(G)$, $I(f + g) \le I(f) + I(g)$. 
+        \item For each $f, f' \in C_c^+(G)$, $I(f + f') \le I(f) + I(f')$. 
     \end{enumerate}
     
     Let $f, f' \in C_c^+(G)$ and $\eps > 0$. By \autoref{lemma:haar-approx}, there exists $V \in \cn_G(1)$ such that for each $g \in E_V$, 
@@ -137,7 +137,7 @@
 
     In which case, $I(f) + I(f') \le I(f + f') + 3\eps$. Since this holds for all $\eps > 0$, 
     \begin{enumerate}[start=4, label=(\roman*)]
-        \item For each $f, f' \in C_c^+(G)$, $I(f + g) \ge I(f) + I(g)$. 
+        \item For each $f, f' \in C_c^+(G)$, $I(f + f') \ge I(f) + I(f')$. 
     \end{enumerate}
 
     Using \autoref{lemma:positive-functional-extension}, $I$ extends to a positive linear functional on $C_c(G; \real)$, with $I(f) > 0$ for all $f \in C_c^+(G) \setminus \bracs{0}$, and