Automatic continuity of concave functions
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- by Roger Howe PDF
- Proc. Amer. Math. Soc. 103 (1988), 1196-1200 Request permission
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.References
- David Gale, Victor Klee, and R. T. Rockafellar, Convex functions on convex polytopes, Proc. Amer. Math. Soc. 19 (1968), 867–873. MR 230219, DOI 10.1090/S0002-9939-1968-0230219-6
- Victor Klee, Some characterizations of convex polyhedra, Acta Math. 102 (1959), 79–107. MR 105651, DOI 10.1007/BF02559569
- R. Tyrrell Rockafellar, Convex analysis, Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, N.J., 1970. MR 0274683
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 1196-1200
- MSC: Primary 90C20; Secondary 26B25, 52A20
- DOI: https://doi.org/10.1090/S0002-9939-1988-0955008-9
- MathSciNet review: 955008