Stepanov theorem for mappings between metric spaces

TL;DR

This paper extends Rademacher-type theorems for Lipschitz maps between metric spaces by proving a Stepanov-type generalization, combining metric differentiability concepts with rectifiable charts.

Contribution

It introduces a Stepanov-type generalization of Rademacher's theorem for metric differentiability in metric measure spaces, building on Kirchheim and Cheeger's frameworks.

Findings

Proves a Stepanov-type theorem for metric differentiability

Extends differentiability results to a broader class of metric maps

Combines ideas from Kirchheim and Cheeger for new insights

Abstract

For Lipschitz maps between a metric measure space and a metric space, combining the ideas of Kirchheim's metric differentiability and Cheeger's differentiable structures leads to a Rademacher-type theorem for a notion of metric differentiability with respect to a rectifiable chart, and in this paper we prove the validity of a Stepanov-type generalization of such result under the same assumptions.