Stepanov theorem for mappings between metric spaces

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.