# Absolutely continuous functions of several variables and diffeomorphisms

Open Mathematics (2003)

- Volume: 1, Issue: 4, page 690-705
- ISSN: 2391-5455

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topStanislav Hencl, and Jan Malý. "Absolutely continuous functions of several variables and diffeomorphisms." Open Mathematics 1.4 (2003): 690-705. <http://eudml.org/doc/268750>.

@article{StanislavHencl2003,

abstract = {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.},

author = {Stanislav Hencl, Jan Malý},

journal = {Open Mathematics},

keywords = {26B30},

language = {eng},

number = {4},

pages = {690-705},

title = {Absolutely continuous functions of several variables and diffeomorphisms},

url = {http://eudml.org/doc/268750},

volume = {1},

year = {2003},

}

TY - JOUR

AU - Stanislav Hencl

AU - Jan Malý

TI - Absolutely continuous functions of several variables and diffeomorphisms

JO - Open Mathematics

PY - 2003

VL - 1

IS - 4

SP - 690

EP - 705

AB - 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.

LA - eng

KW - 26B30

UR - http://eudml.org/doc/268750

ER -

## References

top- [1] M. Csörnyei: “Absolutely continuous functions of Rado, Reichelderfer and Malý”, J. Math. Anal. Appl., Vol. 252, (2000), pp. 147–166. http://dx.doi.org/10.1006/jmaa.2000.6962
- [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 Zbl1002.26007
- [3] S. Hencl: “Absolutely continuous functions of several variables and quasiconformal mappings”, preprint MATH-KMA-2002/89, Charles University, Prague.
- [4] J. Malý: “Absolutely continuous function of several variables”, J. Math. Anal. Appl., Vol. 231, (1999), pp. 492–508. http://dx.doi.org/10.1006/jmaa.1998.6246

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