On strongly measurable Kurzweil-Henstock type integrable functions

Abstract

We consider the integrability, with respect to the scalar Kurzweil-Henstock integral, the Kurzweil-Henstock-Pettis integral and the variational Henstock integral, of strongly measurable functions de ned as f = P1 n=1 xn [n;n+1),where (xn) belongs to a Banach space. Examples which indicate the difference between the scalar Henstock-Kurzweil integral and the Henstock- Kurzweil-Pettis integral and between the variational Henstock integral and the Henstock-Kurzweil-Pettis integral are given.