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# On Whitney-type Characterization of Approximate Differentiability on Metric Measure Spaces

Published:2013-02-08
Printed: Aug 2014
• E. Durand-Cartagena,
Departamento de Matemática Aplicada. ETSI Industriales, UNED c/Juan del Rosal 12 Ciudad Universitaria, 28040 Madrid, Spain
• L. Ihnatsyeva,
Department of Mathematics and Statistics, P.O. Box 68, FI-00014 University of Helsinki, Finland
• R. Korte,
Department of Mathematics and Statistics, P.O. Box 68, FI-00014 University of Helsinki, Finland
• M. Szumańska,
Faculty of Mathematics, Informatics, and Mechanics University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
 Format: LaTeX MathJax PDF

## Abstract

We study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is a Whitney-type characterization of approximately differentiable functions in this setting. As an application, we prove a Stepanov-type theorem and consider approximate differentiability of Sobolev, $BV$ and maximal functions.
 Keywords: approximate differentiability, metric space, strong measurable differentiable structure, Whitney theorem
 MSC Classifications: 26B05 - Continuity and differentiation questions 28A15 - Abstract differentiation theory, differentiation of set functions [See also 26A24] 28A75 - Length, area, volume, other geometric measure theory [See also 26B15, 49Q15] 46E35 - Sobolev spaces and other spaces of smooth'' functions, embedding theorems, trace theorems

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