Strongly Measurable Kurzweil-Henstock Type Integrable Functions and Series

Abstract

We give necessary and sufficient conditions for the scalar Kurzweil-Henstock integrability and the Kurzweil-Henstock-Pettis integrability of functions f : [1, ∞) → X defined as f = ∑^∞ _n=1 x_nχ _[n,n+1). Also the variational Henstock integrability is considered.