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The size of the Dini subdifferential

Authors:	Joë l Benoist

Institution:	Maître de Conférences, LACO, CNRS-ESA 6090, Université de Limoges, 87 060 Limoges, France

Abstract:	Given a lower semicontinuous function $f:\mathbb{R}^h \rightarrow \mathbb{R} \cup \{+\infty\}$ , we prove that the points of $\mathbb{R}^h$ , where the lower Dini subdifferential contains more than one element, lie in a countable union of sets which are isomorphic to graphs of some Lipschitzian functions defined on $\mathbb{R}^{h-1}$ . Consequently, the set of all these points has a null Lebesgue measure.

Keywords:	Lower semicontinuous function Dini subdifferential proximal subdifferential countability null Lebesgue measure set

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