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Henstock-Kurzweil integral on BV sets

Jan Malý, Washek Frank Pfeffer (2016)

Mathematica Bohemica

The generalized Riemann integral of Pfeffer (1991) is defined on all bounded BV subsets of n , but it is additive only with respect to pairs of disjoint sets whose closures intersect in a set of σ -finite Hausdorff measure of codimension one. Imposing a stronger regularity condition on partitions of BV sets, we define a Riemann-type integral which satisfies the usual additivity condition and extends the integral of Pfeffer. The new integral is lipeomorphism-invariant and closed with respect to the formation...

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