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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Bibliographic Details
Published in:Open mathematics (Warsaw, Poland) Vol. 1; no. 4; pp. 690 - 705
Main Authors: Hencl, Stanislav, Malý, Jan
Format: Journal Article
Language:English
Published: Warsaw Versita 01.12.2003
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
De Gruyter
Subjects:
26B30
absolute continuity in several variables
change of variables
Continuity (mathematics)
Cubes
Isomorphism
Mathematical analysis
Tornadoes
ISSN:2391-5455, 2391-5455
Online Access:Get full text
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Summary: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.
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content type line 14
ISSN:2391-5455
2391-5455
DOI:10.2478/BF02475188