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Extending Rademacher Theorem to Set-Valued Maps

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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hal-03896086 , version 1 (13-12-2022)

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Aris Daniilidis, Marc Quincampoix. Extending Rademacher Theorem to Set-Valued Maps. 2022. ⟨hal-03896086⟩
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