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

Abstract

We study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is aWhitney-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. © Canadian Mathematical Society 2013.