Geodesic
The Henstock-Kurzweil approach to Young integrals with integrators in ${\rm BV}\sb \phi$
Mathematica Bohemica, Tome 131 (2006) no. 3, pp. 233-260.

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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.
DOI : 10.21136/MB.2006.134138
Classification : 26A21, 26A39, 26A42, 28B15
Keywords: Henstock integral; Stieltjes integral; Young integral; $\phi $-variation 
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Varayu, Boonpogkrong; Chew, Tuan Seng. The Henstock-Kurzweil approach to Young integrals with integrators in ${\rm BV}\sb \phi$. Mathematica Bohemica, Tome 131 (2006) no. 3, pp. 233-260. doi : 10.21136/MB.2006.134138. http://geodesic.mathdoc.fr/articles/10.21136/MB.2006.134138/

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