On the notions of absolute continuity for functions of several variables
Absolutely continuous functions of $n$ variables were recently introduced by J. Malý . 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.