Lebesgue integrability implies generalized Riemann integrability in \(\mathbb R^{]0,1]}\) (Q1852455)

The Wiener integral is an integral with respect to Wiener measure, shown to be actually a measure by Wiener in 1920's. An integral of Riemann type, using Wiener measure of cylindrical intervals and gauge functions, was defined by Henstock in 1970's. In this paper, it is proved that every Wiener integrable function is Henstock integrable. Conversely, every Wiener measurable nonnegative Henstock integrable function is Wiener integrable. The following open problem is mentioned in the paper: if \(f\) is Henstock integrable, is \(f\) Wiener measurable?