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On the Differentiation of Henstock and McShane Integrals

机译：Henstock的分化和麦克肖恩积分

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摘要

It is well known that the derivative of the primitive of 1-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 1-dimensional McShane integrals, n-dimensional McShane and Henstock integrals, covering theorems of Vitali's type cannot be applied. In this paper, we shall discuss differentiation of n-dimensional McShane and Henstock integrals.
机译：众所周知,的导数原始的维Henstock积分几乎在任何地方都存在。用于Henstock导数点区间双,是一致的点区间双Henstock中使用积分。点,更准确地说,导数不存在的点集与测量零。我们可以将一组Henstock点区间对一组点与测量零因为维塔利的覆盖定理。维麦柯肖恩积分,n维麦克肖恩和Henstock积分,覆盖定理维塔利的类型不能应用。纸,我们将讨论的分化n维麦柯肖恩和Henstock积分。

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