Absolutely continuous functions of n variables were recently introduced by J. Malý [5]. We introduce a more general definition, suggested by L. Zajíček. This new absolute continuity also implies continuity, weak differentiability with gradient in Lⁿ, differentiability almost everywhere and the area formula. It is shown that our definition does not depend on the shape of balls in the definition.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm173-2-5,
author = {Stanislav Hencl},
title = {On the notions of absolute continuity for functions of several variables},
journal = {Fundamenta Mathematicae},
volume = {173},
year = {2002},
pages = {175-189},
zbl = {1002.26007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm173-2-5}
}
Stanislav Hencl. On the notions of absolute continuity for functions of several variables. Fundamenta Mathematicae, Tome 173 (2002) pp. 175-189. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm173-2-5/