ON KURZWEIL-HENSTOCK-PETTIS AND KURZWEIL-HENSTOCK INTEGRALS OF BANACH SPACE-VALUED FUNCTIONS

Abstract

In this paper we discuss the relationship between the Kurzweil-Henstock-Pettis and Kurzweil-Henstock integrals in Banach spaces. We prove that in Schur spaces the Kurzweil-Henstock-Pettis and Kurzweil-Henstock integrability for measurable functions satisfying the condition $(C)$ are equivalent. In particular, in Schur spaces the Kurzweil-Henstock-Dunford, Kurzweil-Henstock-Pettis and Kurzweil-Henstock integrability for measurable functions satisfying the condition $(C)$ are equivalent.