Absolutely continuous functions of several variables and diffeomorphisms

In [4], a class of absolutely continuous functions of d-variables, motivated by applications to change of variables in an integral, has been introduced. The main result of this paper states that absolutely continuous functions in the sense of [4] are not stable under diffeomorphisms. We also show an...

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Vydáno v:Open mathematics (Warsaw, Poland) Ročník 1; číslo 4; s. 690 - 705
Hlavní autoři: Hencl, Stanislav, Malý, Jan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Warsaw Versita 01.12.2003
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
De Gruyter
Témata:
26B30
absolute continuity in several variables
change of variables
Continuity (mathematics)
Cubes
Isomorphism
Mathematical analysis
Tornadoes
ISSN:2391-5455, 2391-5455
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Popis
Shrnutí:In [4], a class of absolutely continuous functions of d-variables, motivated by applications to change of variables in an integral, has been introduced. The main result of this paper states that absolutely continuous functions in the sense of [4] are not stable under diffeomorphisms. We also show an example of a function which is absolutely continuous with respect cubes but not with respect to balls.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:2391-5455
2391-5455
DOI:10.2478/BF02475188