On the notions of absolute continuity for functions of several variables

@article{StanislavHencl2002,
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 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.},
author = {Stanislav Hencl},
journal = {Fundamenta Mathematicae},
keywords = {absolute continuity; weak differentiability; differentiability almost everywhere; area formula},
language = {eng},
number = {2},
pages = {175-189},
title = {On the notions of absolute continuity for functions of several variables},
url = {http://eudml.org/doc/283143},
volume = {173},
year = {2002},
}

TY - JOUR
AU - Stanislav Hencl
TI - On the notions of absolute continuity for functions of several variables
JO - Fundamenta Mathematicae
PY - 2002
VL - 173
IS - 2
SP - 175
EP - 189
AB - 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.
LA - eng
KW - absolute continuity; weak differentiability; differentiability almost everywhere; area formula
UR - http://eudml.org/doc/283143
ER -