Refinement of the Benoist theorem on the size of Dini subdifferentials
نویسندگان
چکیده
Given a lower semicontinuous function f : Rn → R ∪ {+∞}, we prove that the set of points of Rn where the lower Dini subdifferential has convex dimension k is countably (n − k)-rectifiable. In this way, we extend a theorem of Benoist(see [1, Theorem 3.3]), and as a corollary we obtain a classical result concerning the singular set of locally semiconcave functions.
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