KURZWEIL-HENSTOCK AND KURZWEIL-HENSTOCK-PETTIS INTEGRABILITY OF STRONGLY MEASURABLE FUNCTIONS

We study the integrability of Banach valued strongly measurable functions defined on [0, 1]. In case of functions f given by Sigma(infinity)(n=1) x(n chi)E(n), where x(n) belong to a Banach space and the sets E-n are Lebesgue measurable and pairwise disjoint subsets of [0, 1], there are well known characterizations for the Bochner and for the Pettis integrability of f (cf Musial (1991)). In this paper we give some conditions for the Kurzweil-Henstock and the Kurzweil-Henstock-Pettis integrability of such functions.