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.
@article{bwmeta1.element.doi-10_2478_BF02475188,
author = {Stanislav Hencl and Jan Mal\'y},
title = {Absolutely continuous functions of several variables and diffeomorphisms},
journal = {Open Mathematics},
volume = {1},
year = {2003},
pages = {690-705},
zbl = {1033.26020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475188}
}
Stanislav Hencl; Jan Malý. Absolutely continuous functions of several variables and diffeomorphisms. Open Mathematics, Tome 1 (2003) pp. 690-705. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475188/
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[2] S. Hencl: “On the notions of absolute continuity for functions of several variables”, Fund. Math., Vol. 173, (2002), pp. 175–189. http://dx.doi.org/10.4064/fm173-2-5 | Zbl 1002.26007
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