Extending Rademacher Theorem to Set-Valued Maps

2022/12/13 by Daniilidis, Aris, Quincampoix, Marc · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2212.06690

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.

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• Gamma-Convergence of Convex Functions, Conjugates, and Subdifferentials

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