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On Whitney-type Characterization of Approximate Differentiability on Metric Measure Spaces
Published online by Cambridge University Press: 20 November 2018
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.
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- Research Article
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- Copyright © Canadian Mathematical Society 2014
Footnotes
The first author was partially supported by grant MTM2009-07848 (Spain). The second, the third and the fourth authors were supported by the Academy of Finland (grants 252293, 250403 and 138738). The fourth author was partially supported by MNiSW Grant no N N201 397737, Nonlinear partial differential equations: geometric and variational problems.
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