Extending Rademacher Theorem to Set-Valued Maps
Classical Analysis and ODEs
2022-12-14 v1 Optimization and Control
Abstract
Rademacher theorem asserts that Lipschitz continuous functions between Euclidean spaces are differentiable almost everywhere. In this work we extend this result to set-valued maps using an adequate notion of set-valued differentiability relating to convex processes. Our approach uses Rademacher theorem but also recovers it as a special case.
Cite
@article{arxiv.2212.06690,
title = {Extending Rademacher Theorem to Set-Valued Maps},
author = {Aris Daniilidis and Marc Quincampoix},
journal= {arXiv preprint arXiv:2212.06690},
year = {2022}
}