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Start Over Creator Skvortsov, Valentin A.

1. On McShane-type integrals with respect to some derivation bases

Creator:
Skvortsov, Valentin A. and Sworowski, Piotr
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
McShane integral, Kurzweil-Henstock integral, Perron integral, and basis
Language:
English
Description:
Some observations concerning McShane type integrals are collected. In particular, a simple construction of continuous major/minor functions for a McShane integrand in Rn is given.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. The AP-Denjoy and AP-Henstock integrals revisited

Creator:
Skvortsov, Valentin A. and Sworowski, Piotr
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
approximate Kurzweil-Henstock integral, approximate continuity, local system, and variational measure
Language:
English
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public