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
Marraffa, V. (2008). A characterization of strongly measurable Henstock-Kurzweil integrable functions and weakly continuous operators. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 340(2), 1171-1179 [10.1016/j.jmaa.2007.09.033].
A characterization of strongly measurable Henstock-Kurzweil integrable functions and weakly continuous operators
MARRAFFA, Valeria
2008-01-01
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
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