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

Let f   be a function defined on [0,1][0,1] and taking values in a Banach space X  . We show that the limit set IHK(f)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.