The AP-Denjoy and AP-Henstock integrals revisited

Title:

The AP-Denjoy and AP-Henstock integrals revisited

Creator:

Skvortsov, Valentin A. and Sworowski, Piotr

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:198645e0-c23f-4f3e-b4fd-e5cbc0e1a38f
uuid:198645e0-c23f-4f3e-b4fd-e5cbc0e1a38f

Subject:

approximate Kurzweil-Henstock integral, approximate continuity, local system, and variational measure

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The note is related to a recently published paper J. M. Park, J. J. Oh, C.-G. Park, D. H. Lee: The AP-Denjoy and AP-Henstock integrals. Czech. Math. J. 57 (2007), 689–696, which concerns a descriptive characterization of the approximate Kurzweil-Henstock integral. We bring to attention known results which are stronger than those contained in the aforementioned work. We show that some of them can be formulated in terms of a derivation basis defined by a local system of which the approximate basis is known to be a particular case. We also consider the relation between the $\sigma $-finiteness of variational measure generated by a function and the classical notion of the generalized bounded variation.

Language:

English

Rights:

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

Coverage:

581-591

Source:

Czechoslovak Mathematical Journal | 2012 Volume:62 | Number:3

Harvested from:

CDK

Metadata only:

false