Abstract
The generalized Riemann integral of Pfeffer (1991) is defined on all bounded BV subsets of R 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 of improper integrals. Its definition in R coincides with the Henstock-Kurzweil definition of the Denjoy-Perron integral.