Fixed typos in the gluing lemma.

src/measure/measurable-maps/approx.tex

@@ -38,6 +38,7 @@
     \begin{enumerate}
         \item $\seq{I_n}$ is an $\mathcal{A}$-admissible \hyperref[approximation of the identity]{definition:approximation-id-measure}. 
         \item For each $N \in \natp$, $I_N$ is Borel measurable with $I_N(X) \subset \bracsn{x_n|1 \le n \le N}$. 
+        \item For each $n \in \natp$ and $x \in X$, $d(x, I_{n+1}(x)) \le d(x, I_n(x))$. 
     \end{enumerate}
 \end{lemma}
 \begin{proof}
@@ -83,7 +84,7 @@
 
     Finally, for each $x \in X$ and $\eps > 0$, since $x \in \ol{\mathcal{A}(x)^o}$, there exists $N_0 \in \natp$ such that $x_{N_0} \in \mathcal{A}(x)$ and $d(x, x_{N_0}) < \eps$. In which case, for any $N \ge N_0$, $N_0 \in C_N(x)$ and $d(x, I_N(x)) \le d(x, x_{N_0}) < \eps$. Thus $I_N(x) \to x$ as $N \to \infty$, and $\seq{I_N}$ satisfies (AI1). 
     
-    Therefore $\seq{I_N}$ is an approximation of the identity satisfying (1) and (2). 
+    Therefore $\seq{I_N}$ is an approximation of the identity satisfying (1)-(3). 
 \end{proof}