Generic differentiability of Lipschitzian functions

Lebourg, G.

doi:10.1090/S0002-9947-1979-0546911-1

Generic differentiability of Lipschitzian functions
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by G. Lebourg PDF

Trans. Amer. Math. Soc. 256 (1979), 125-144 Request permission

Abstract:

It is shown that, in separable topological vector spaces which are Baire spaces, the usual properties that have been introduced to study the local “first order” behaviour of real-valued functions which satisfy a Lipschitz type condition are “generically” equivalent and thus lead to a unique class of “generically smooth” functions. These functions are characterized in terms of tangent cones and directional derivatives and their “generic” differentiability properties are studied. The results extend some of the well-known differentiability properties of continuous convex functions.

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Intégration des mésures, Éléments de mathématique

Intégration

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