Remarks on the Henstock Integral of Stieltjes Type

Abstract

Let f:[a, b]→ R be bounded and g:[a, b]→ R be of bounded variation.It is shown that f is Henstock integrable with respect to g on [a, b] if and only if f is Young refinement integrable with respect g on [a, b], and both integrals have the same value.Some relations to the mean Stieltjes integral will also be given.