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

Durand-Cartagena, E. ; Ihnatsyeva, L. ; Korte, R. ; Szumańska, M.

Canadian journal of mathematics, Tome 66 (2014) no. 4, pp. 721-742

Résumé

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.

Détail

DOI : 10.4153/CJM-2012-064-x

Mots-clés : 26B05, 28A15, 28A75, 46E35, approximate differentiability, metric space, strong measurable differentiable structure,Whitney theorem

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