A HENSTOCK-KURZWEIL INTEGRABLE VECTOR-VALUED FUNCTION WHICH IS NOT MCSHANE INTEGRABLE ON ANY PORTION

摘要

We give an example of a function from [a, b] into Co, which is Henstock-Kurzweil integrable on [a,b] and not McShane integrable on any nondegenerate subinterval of [a, 6]. As a result, any Henstock-Kurzweil integrable function from [a, b] into a Banach space X is McShane integrable on some nondegenerate subinterval of [a, b] if and only if X contains no isomorphic copy of c_0 .