Description of the limit set of Henstock-Kurzweil integral sums of vector-valued functions

Abstract

Let f be a function defined on [0, 1] and taking values in a Banach space X. We show that the limit set IHK(f) of Henstock-Kurzweil integral sums is non-empty and convex when the function f has an integrable majorant and X is separable. In the same setting we give a complete description of the limit set.