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

 

A class of strong differentiability spaces


Author: James B. Collier
Journal: Proc. Amer. Math. Soc. 53 (1975), 420-422
MSC: Primary 46B05
MathSciNet review: 0388044
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Abstract: It is shown that if the dual of a Banach space $ X$ is weakly compactly generated, then each convex function on $ X$ is Fréchet differentiable on a dense $ {G_\delta }$ subset of its domain of continuity.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0388044-5
PII: S 0002-9939(1975)0388044-5
Keywords: Fréchet differentiability, convex function, strongly exposed point
Article copyright: © Copyright 1975 American Mathematical Society