On Henstock–Kurzweil and McShane integrals of Banach space-valued functions

This paper deals with the relation between the McShane integral and the Henstock–Kurzweil integral for the functions mapping a compact interval I0 ⊂ Rm into a Banach space X and some other questions in connection with the McShane integral and the Henstock–Kurzweil integral of Banach space-valued functions. We prove that if a Banach space-valued function f is Henstock–Kurzweil integrable on I0 and satisfies Property (P), then I0 can be written as a countable union of closed sets En such that f is McShane integrable on each En when X contains no copy of c0. We further give an answer to the Karták’s question. © 2006 Elsevier Inc. All rights reserved.