Geodesic
Typical Convexity (Concavity) of Dini-Hadamard Upper (Lower) Directional Derivatives of Functions on Separable Banach Spaces
Journal of convex analysis, Tome 17 (2010) no. 3, pp. 1019-1032.

Voir la notice de l'article provenant de la source Heldermann Verlag

By "typical" we mean "valid outside a small (or negligible) set". There are various concepts of "smallness" used in analysis: measure theoretic (null sets of different kind), topological (sets of the first Baire category), metric (σ-porous sets or directionally σ-porous sets), analytic (countable unions of sets that can be represented as (subsets of) graphs of certain classes of Lipschitz functions). 
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     author = {A. Ioffe},
     title = {Typical {Convexity} {(Concavity)} of {Dini-Hadamard} {Upper} {(Lower)} {Directional} {Derivatives} of {Functions} on {Separable} {Banach} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {1019--1032},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a17/}
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A. Ioffe. Typical Convexity (Concavity) of Dini-Hadamard Upper (Lower) Directional Derivatives of Functions on Separable Banach Spaces. Journal of convex analysis, Tome 17 (2010) no. 3, pp. 1019-1032. http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a17/