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.
Keywords
Set-valued map graphical derivative convex process Lipschitz continuity Rademacher theorem AMS Classification: Primary: 26E25 28A15
Secondary: 49J53 49J52
Set-valued map
graphical derivative
convex process
Lipschitz continuity
Rademacher theorem AMS Classification: Primary: 26E25
28A15
Secondary: 49J53
49J52
Origin : Files produced by the author(s)