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

TL;DR

This paper provides a Whitney-type characterization of approximately differentiable functions on metric measure spaces with a Cheeger differentiable structure, extending classical concepts and applying them to Sobolev, BV, and maximal functions.

Contribution

It introduces a new Whitney-type criterion for approximate differentiability in metric measure spaces with Cheeger structures, linking it to classical analysis.

Findings

Established a Whitney-type characterization for approximate differentiability.

Proved a Stepanov-type theorem in this setting.

Analyzed approximate differentiability of Sobolev, BV, and maximal functions.

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.