diff --git a/src/fa/lp/ui.tex b/src/fa/lp/ui.tex
index 2c2a971..b567855 100644
--- a/src/fa/lp/ui.tex
+++ b/src/fa/lp/ui.tex
@@ -201,7 +201,7 @@
     (UI): Let $\eps > 0$. By (N) and (T), there exists $F_1 \in \fF$ and $A \in \cm$ with $\mu(A) < \infty$ such that for every $f \in F_1$, 
     \begin{enumerate}[label=(\roman*)]
         \item $|\norm{f}_{L^p(X; E)}^p - \norm{g}_{L^p(X; E)}^p| < \eps$. 
-        \item $\int_{A^c}\norm{f}_E^p d\mu < \eps$ and $\int_{A^c}\norm{g}_E^p d\mu$. 
+        \item $\int_{A^c}\norm{f}_E^p d\mu, \int_{A^c}\norm{g}_E^p d\mu < \eps$. 
     \end{enumerate}
     
     By (i) and (ii), 
@@ -221,7 +221,7 @@
         \item $\mu(A \cap \bracs{\norm{f - g}_E > \delta}) < \delta$. 
     \end{enumerate}
     
-    Let $B \in \cm$ with $B \subset A$ and $\mu(B) < \delta$, then for any $f \in F_3$, 
+    Let $B \in \cm$ with $B \subset A$ and $\mu(B) < \delta$, then for any $f \in F_2$, 
     \begin{align*}
         \int_{A \setminus B}\norm{f}_E^p d\mu &\ge \int_{(A \setminus B) \cap \bracs{\norm{f - g}_E \le \delta}}\norm{f}_E^p d\mu \\
         &\ge \int_{(A \setminus B) \cap \bracs{\norm{f - g}_E \le \delta}}(\norm{g}_E - \delta \vee 0)^pd\mu \\
@@ -250,7 +250,7 @@
 
     so $\int_{B}\norm{f}_E^p d\mu \le 6\eps$ for all $B \in \cm$ with $B \subset A$ and $\mu(B) < \delta$.
     
-    Finally, by (i) and \hyperref[Markov's Inequality]{theorem:markov-inequality}, there exists $M \ge 0$ such that $\mu\bracs{\norm{f}_E \ge M} < \delta$ for all $f \in F_3$. Therefore for any $f \in F_3$, 
+    Finally, by (i) and \hyperref[Markov's Inequality]{theorem:markov-inequality}, there exists $M \ge 0$ such that $\mu\bracs{\norm{f}_E \ge M} < \delta$ for all $f \in F_2$. Therefore for any $f \in F_2$, 
     \[
         \int_{\bracs{\norm{f}_E \ge M}}\norm{f}_E^p d\mu \le \int_{A \cap \bracs{\norm{f}_E \ge M}}\norm{f}_E^p d\mu + \int_{A^c}\norm{f}_E^p d\mu \le 7\eps
     \]