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
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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).
@article{JCA_2010_17_3_JCA_2010_17_3_a17,
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/}
}
TY - JOUR AU - A. Ioffe TI - Typical Convexity (Concavity) of Dini-Hadamard Upper (Lower) Directional Derivatives of Functions on Separable Banach Spaces JO - Journal of convex analysis PY - 2010 SP - 1019 EP - 1032 VL - 17 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a17/ ID - JCA_2010_17_3_JCA_2010_17_3_a17 ER -
%0 Journal Article %A A. Ioffe %T Typical Convexity (Concavity) of Dini-Hadamard Upper (Lower) Directional Derivatives of Functions on Separable Banach Spaces %J Journal of convex analysis %D 2010 %P 1019-1032 %V 17 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a17/ %F JCA_2010_17_3_JCA_2010_17_3_a17
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/