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Keywords:
Henstock integral; Stieltjes integral; Young integral; $\phi $-variation
Summary:
In 1938, L. C. Young proved that the Moore-Pollard-Stieltjes integral $\int _a^bf\mathrm{d}g$ exists if $f\in \mathop {{\mathrm BV}}_\phi [a,b]$, $g\in \mathop {{\mathrm BV}}_\psi [a,b]$ and $\sum _{n=1}^\infty \phi ^{-1}({1}/{n})\psi ^{-1} ({1}/{n})<\infty $. In this note we use the Henstock-Kurzweil approach to handle the above integral defined by Young.
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