Progress over the past week.

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Bokuan Li
2026-01-05 20:10:39 -05:00
parent e8d394a2ac
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\section{Riemann-Stieltjes Integrals and Functions of Bounded Variationo}
\section{Riemann-Stieltjes Integrals and Functions of Bounded Variation}
\label{section:rs-bv}
\begin{proposition}
@@ -36,7 +36,7 @@
then $f \in RS([a, b], G)$ and $\int_a^b f dG = \lim_{\alpha \in A}\int_a^b f_\alpha dG$. In particular,
\begin{enumerate}
\item If $H$ is complete, then condition (a) may be omitted.
\item If $H$ is sequentially complete and $A = \nat$, then condition (b) may be omitted.
\item If $H$ is sequentially complete and $A = \nat^+$, then condition (b) may be omitted.
\end{enumerate}
\end{proposition}
\begin{proof}