On Henstock-Wiener integral (Q5929663)

If a generalized Riemann integral is defined with no restriction on the placing of the tags we get the McShane integral, while if each tag is required to be in the sub-interval of it tags we get the Henstock, or Henstock-Kurzweil, integral. It is well known, but not easily proved, that absolutely Henstock integrable functions are McShane integrable. The same result holds if the integrals are defined in the \(n\)-dimensional Euclidean space. This note extends this result to infinite dimensional spaces, when we get the Henstock-Wiener and McShane-Wiener integrals. There are several methods by which the one-dimensional case is extended to higher dimension and the authors show that one of these [\textit{T.-S. Chew, W.-K. Wong} and \textit{G.-C. Tan}, Real Anal. Exch. 23, No. 2, 799-803 (1997; Zbl 0943.26029)], can be adapted to the infinite dimensional case.