On the notions of absolute continuity for functions of several variables

Volume 173 / 2002

Stanislav Hencl Fundamenta Mathematicae 173 (2002), 175-189 MSC: Primary 26B30; Secondary 26B10. DOI: 10.4064/fm173-2-5

Abstract

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.

Authors

  • Stanislav HenclDepartment of Mathematical Analysis
    Charles University
    Sokolovská 83
    186 00 Praha 8, Czech Republic
    e-mail

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