A Variational Integral for Banach-Valued Functions

It is shown that for Banach–space–valued functions the variational Henstock integral is equivalent to the Henstock integral if and only if the range space is of a finite dimension. The same is true for the equivalence of the variational McShane integral and the McShane integral. There ] a closed interval on the line, and by | E | Lebesgue measure of a set E