On the notions of absolute continuity for functions of several variables

• Autorzy: Stanislav Hencl
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 26B10: Implicit function theorems, Jacobians, transformations with several variables
• 26B30: Absolutely continuous functions, functions of bounded variation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 173
• Numer: 2
• Strony: 175-189

Daty

wydano

2002

Twórcy

autor

Stanislav Hencl

• Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 00 Praha 8, Czech Republic

Identyfikatory

DOI

10.4064/fm173-2-5