Geodesic
On the notions of absolute continuity for functions of several variables
Stanislav Hencl1
1 Department of Mathematical Analysis Charles University Sokolovská 83 186 00 Praha 8, Czech Republic
Fundamenta Mathematicae, Tome 173 (2002) no. 2, pp. 175-189.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $L^n$, differentiability almost everywhere and the area formula. It is shown that our definition does not depend on the shape of balls in the definition.
DOI : 10.4064/fm173-2-5
Keywords: absolutely continuous functions variables recently introduced mal introduce general definition suggested zaj absolute continuity implies continuity weak differentiability gradient differentiability almost everywhere area formula shown definition does depend shape balls definition

Stanislav Hencl 1

1 Department of Mathematical Analysis Charles University Sokolovská 83 186 00 Praha 8, Czech Republic 
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Stanislav Hencl. On the notions of absolute continuity for
 functions of several variables. Fundamenta Mathematicae, Tome 173 (2002) no. 2, pp. 175-189. doi : 10.4064/fm173-2-5. http://geodesic.mathdoc.fr/articles/10.4064/fm173-2-5/

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