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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Fréchet differentiation of convex functions in a Banach space with a separable dual


Authors: D. Preiss and L. Zajíček
Journal: Proc. Amer. Math. Soc. 91 (1984), 202-204
MSC: Primary 46G05
MathSciNet review: 740171
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Abstract: Let $ X$ be a real Banach space with a separable dual and let $ f$ be a continuous convex function on $ X$. We sharpen the well-known result that the set of points at which $ f$ is not Fréchet differentiable is a first category set by showing that it is even $ \sigma $-porous. On the other hand, a simple example shows that this set need not be a null set for any given Radon measure.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0740171-1
PII: S 0002-9939(1984)0740171-1
Article copyright: © Copyright 1984 American Mathematical Society