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On Whitney-type characterization of approximate differentiability on metric measure spaces

  • 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
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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 approximate differentiability, metric space, strong measurable differentiable structure, Whitney theorem
MSC Classifications: 26B05, 28A15, 28A75, 46E35 show english descriptions Continuity and differentiation questions
Abstract differentiation theory, differentiation of set functions [See also 26A24]
Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]
Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
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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