Nearly upper semicontinuous gauge functions in \({\mathbb{R}}^ m\)
The basic result of this paper is that in defining generalized Riemann integrals by the method of Henstock-Kurzweil it suffices that the gauge function be upper semicontinuous on the complement of a set of measure zero (in particular we can assume the gauge is measurable). This result is due to Pfeffer but his proof uses methods valid in one dimension only. The present author gives a proof that translates easily to higher dimensions. It is known that the gauge function need not be upper semicontinuous everywhere [\textit{J. Foran} and \textit{S. Meinershagen}, Real Anal. Exch. 13(1987/88), 265-277 (1988)].
higher dimensional Henstock-Kurzweil integral
scientific article; zbMATH DE number 4071248