On the notions of absolute continuity for functions of several variables
Volume 173 / 2002
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.
