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\section{Riemann-Stieltjes Integrals and Functions of Bounded Variationo}
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\section{Riemann-Stieltjes Integrals and Functions of Bounded Variation}
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\label{section:rs-bv}
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\begin{proposition}
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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,
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\begin{enumerate}
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\item If $H$ is complete, then condition (a) may be omitted.
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\item If $H$ is sequentially complete and $A = \nat$, then condition (b) may be omitted.
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\item If $H$ is sequentially complete and $A = \nat^+$, then condition (b) may be omitted.
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\end{enumerate}
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\end{proposition}
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\begin{proof}
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