Fixed some typos.

src/fa/rs/rs-bv.tex

@@ -123,7 +123,7 @@
     \end{align*}
 
 
-    Since $\alpha \in BV([a, b]; F)$, by \autoref{proposition:rs-bv-continuous}, for any $\seq{(P_n, c_n)} \subset \scp_t([a, b])$, 
+    Since $f \in C([a, b] \times [c, d]; E)$, $f$ is uniformly continuous by \autoref{proposition:uniform-continuous-compact}, and $\bracs{f(\cdot, t)|t \in [c, d]} \subset C([a, b]; E)$ is uniformly equicontinuous. As $\alpha \in BV([a, b]; F)$, by \autoref{proposition:rs-bv-continuous}, for any $\seq{(P_n, c_n)} \subset \scp_t([a, b])$, 
     \[
     \int_a^b \int_c^d f(s, t) \beta(dt) \alpha(ds) = \limv{n}S(P_n, c, g, \alpha)
     \]
@@ -133,7 +133,7 @@
     \limv{n}S(P_n, c_n, f(\cdot, t), \alpha) = \int_a^b f(s, t) \alpha(ds)
     \]
 
-    uniformly for all $t \in [c, d]$. Since $f \in C([a, b] \times [c, d]; E)$, $f$ is uniformly continuous by \autoref{proposition:uniform-continuous-compact}, and $\bracs{f(\cdot, t)|t \in [c, d]} \subset C([a, b]; E)$ is uniformly equicontinuous. As $\beta \in BV([c, d]; G)$, 
+    uniformly for all $t \in [c, d]$. Finally, given that $\beta \in BV([c, d]; G)$, 
     \[
     \int_c^d\int_a^b f(s, t) \alpha(ds) \beta(dt) = \limv{n}\int_c^d S(P_n, c_n, f(\cdot, t), \alpha) \beta(dt)
     \]

src/fa/tvs/complexify.tex

@@ -14,7 +14,7 @@
         E \ar@{->}[u]^{\iota} \ar@{->}[ru]_{T} & 
         }
         \]
-        \item $\complex(E) = \iota(E) \oplus i\iota(E)$ as a vector space over $\real$. For each $z \in \complex(E)$ with $z = x + iy$, $x = \text{Re}(x)$ and $y = \text{Re}(y)$ are the \textbf{real} and \textbf{imaginary parts} of $z$. 
+        \item $\complex(E) = \iota(E) \oplus i\iota(E)$ as a vector space over $\real$. For each $z \in \complex(E)$ with $z = x + iy$, $x = \text{Re}(x)$ and $y = \text{Im}(y)$ are the \textbf{real} and \textbf{imaginary parts} of $z$. 
     \end{enumerate}
 
     The pair $(\complex(E), \iota)$ is the \textbf{complexification} of $E$, and