Henstock积分问题的一个注记

摘要

本文证明了如果X是不含c0的Banach空间,f是定义在区间I0(C) Rm上取值于Banach空间X的函数,并且f在I0上Henstock可积,则总存在I0的一个非退化子区间J,使得f在J上McShane可积,从而对Karták的一个问题作出了肯定的回答.%If a Banach space-valued function f defined on I0 (C) Rm is Henstock integrable, then one can always find a nondegenerate subinterval J (C) Io on which f is McShane integrable when X contains no copy of co. So we give an affirmative answer to a problem proposed by Karták.