Journal of convex analysis, Tome 17 (2010) no. 3, pp. 1019-1032
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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/
@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},
year = {2010},
volume = {17},
number = {3},
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
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
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%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
%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
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).
