BANACH-VALUED HENSTOCK-KURZWEIL INTEGRABLE FUNCTIONS ARE MCSHANE INTEGRABLE ON A PORTION

It is shown that a Banach-valued Henstock- Kurzweil integrable function on an m-dimensional compact interval is McShane integrable on a portion of the interval. As a consequence, there exist a non-Perron integrable function f : [0, 1](2) -> R and a continuous function F : [0, 1](2) -> R such that (p)integral(x)(0) {(p) integral(y)(0) f(u,v) du = (p)integral(y)(0) { (p) integral(x)(0) f(u,v)du}dv =f(x,y) for all (x, y) is an element of[0, 1](2).