Geodesic
Henstock-Kurzweil integral on ${\rm BV}$ sets
Mathematica Bohemica, Tome 141 (2016) no. 2, pp. 217-237.

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The generalized Riemann integral of Pfeffer (1991) is defined on all bounded $\rm BV$ subsets of $\mathbb R^n$, but it is additive only with respect to pairs of disjoint sets whose closures intersect in a set of $\sigma $-finite Hausdorff measure of codimension one. Imposing a stronger regularity condition on partitions of $\rm BV$ 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 of improper integrals. Its definition in $\mathbb R$ coincides with the Henstock-Kurzweil definition of the Denjoy-Perron integral.
DOI : 10.21136/MB.2016.16
Classification : 26B20, 28A25
Keywords: Henstock-Kurzweil integral; charge; $\rm BV$ set 
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Malý, Jan; Pfeffer, Washek F. Henstock-Kurzweil integral on ${\rm BV}$ sets. Mathematica Bohemica, Tome 141 (2016) no. 2, pp. 217-237. doi : 10.21136/MB.2016.16. http://geodesic.mathdoc.fr/articles/10.21136/MB.2016.16/

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