In 1938, L. C. Young proved that the Moore-Pollard-Stieltjes integral ${\int }_a^{b}f\mathrm{d}g$ exists if $f\in {\mathrm{B}V}_{\phi }[a,b]$, $g\in {\mathrm{B}V}_{\psi }[a,b]$ 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.

This paper generalizes the results of papers which deal with the Kurzweil-Henstock construction of an integral in ordered spaces. The definition is given and some limit theorems for the integral of ordered group valued functions defined on a Hausdorff compact topological space $T$ with respect to an ordered group valued measure are proved in this paper.