Henstock-Kurzweil integral on BV sets

Title:

Henstock-Kurzweil integral on BV sets

Creator:

Malý, Jan and Pfeffer, Washek F.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:33e019f2-25a0-4082-a8dd-5a688098c095
uuid:33e019f2-25a0-4082-a8dd-5a688098c095
doi:10.21136/MB.2016.16

Subject:

Henstock-Kurzweil integral, charge, and BV set

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

217-237

Source:

Mathematica bohemica | 2016 Volume:141 | Number:2

Harvested from:

CDK

Metadata only:

false