On the Differentiation of Henstock and McShane Integrals
It is well known that the derivative of the primitive of one-dimensional Henstock integral exists almost everywhere. Point -interval pairs used in the derivative are Henstock point-interval pairs; which are consistent with point-interval pairs used in the Henstock integral. Note that almost everywhere" is a set of points; more precisely; the derivative does not exist on a set of points with measure zero. We can transform a set of Henstock point-interval pairs to a set of points with measure zero because of Vitali's covering theorem. For one-dimensional McShane integrals; n-dimensional McShane and Henstock integrals; covering theorems of the Vitali type cannot be applied. In this paper; we shall discuss differentiation of n-dimensional McShane and Henstock integrals."
Chew, T. S., Cabral, E. A., & Benitez, J. V. (2021). On the differentiation of Henstock and McShane integrals. Proceedings of the Singapore National Academy of Science, 15(1), 3–8. https://doi.org/10.1142/S2591722621400019