In 1938, L. C. Young proved that the Moore-Pollard-Stieltjes integral R b a f dg exists if f ∈ BVϕ[a, b], g ∈ BVψ[a, b] and ∑∞ n=1 ϕ −1 (1/n)ψ −1 (1/n) < ∞. In this note we use the Henstock-Kurzweil approach to handle the above integral defined by Young.
We propose an extended version of the Kurzweil integral which contains both the Young and the Kurzweil integral as special cases. The construction is based on a reduction of the class of δ-fine partitions by excluding small sets.