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

 

Automatic continuity of concave functions


Author: Roger Howe
Journal: Proc. Amer. Math. Soc. 103 (1988), 1196-1200
MSC: Primary 90C20; Secondary 26B25, 52A20
MathSciNet review: 955008
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Abstract: A necessary and sufficient condition is given that a semicontinuous, nonnegative, concave function on a finite dimensional closed convex set $ X$ necessarily be continuous at a point $ {x_0} \in X$. Application of this criterion at all points of $ X$ yields a characterization, due to Gale, Klee and Rockafellar, of convex polyhedra in terms of continuity of their convex functions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0955008-9
PII: S 0002-9939(1988)0955008-9
Keywords: Concave function, semicontinuity, continuity
Article copyright: © Copyright 1988 American Mathematical Society