Abstract
This paper deals with the relation between the McShane integral and the Henstock–Kurzweil integral for the functions mapping a compact interval I 0 ⊂ R m 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 I 0 and satisfies Property (P), then I 0 can be written as a countable union of closed sets E n such that f is McShane integrable on each E n when X contains no copy of c 0 . We further give an answer to the Karták's question.
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