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Variational measures and the Kurzweil-Henstock integral

SYSNO ASEP	0334190
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Variational measures and the Kurzweil-Henstock integral
Title	Variační míry a Kurzweilův-Henstockův integrál
Author(s)	Schwabik, Štefan (MU-W)_{RID, SAI}
Source Title	Mathematica Slovaca. - : Walter de Gruyter - ISSN 0139-9918 Roč. 59, č. 6 (2009), s. 731-752
Number of pages	22 s.
Language	eng - English
Country	SK - Slovakia
Keywords	variational measure ; Kurzweil-Henstock integral
Subject RIV	BA - General Mathematics
R&D Projects	IAA100190702 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR)
CEZ	AV0Z10190503 - MU-W (2005-2011)
UT WOS	000271672800008
DOI	10.2478/s12175-009-0160-1
Annotation	For a given continuous function F on a compact interval E in the set a"e of reals the problem is how to describe the "total change" of F on a set M aS, E. Full variational measures W (F) (M) and V (F) (M) (see Section 2) in the sense presented by B. S. Thomson are introduced in this work to this aim. They are generated by two slightly different interval functions, namely the oscillation of F over an interval and the value of the additive interval function generated by F, respectively. They coincide with the concept of classical total variation if M is an interval and they are zero if on the set M the function F is of negligible variation. The Kurzweil-Henstock integration is shortly described and some of its properties are studied using the variational measure W (F) (M) for the indefinite integral F of an integrable function f.
Workplace	Mathematical Institute
Contact	Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757
Year of Publishing	2010

Number of the records: 1