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VALERIA MARRAFFA

A characterization of strongly measurable Henstock-Kurzweil integrable functions and weakly continuous operators

Abstract

We give necessary and sufficient conditions for the Kurzweil–Henstock integrability of functions given by f =n=1 xnχEn , where xn belong to a Banach space and the sets (En)n are measurable and pairwise disjoint. Also weakly completely continuous operators between Banach spaces are characterized by means of scalarly Kurzweil–Henstock integrable functions