Title

On the Differentiation of Henstock and McShane Integrals

Document Type

Article

Publication Date

3-8-2021

Abstract

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."

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