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On set correspondences into uniformly convex Banach spaces

Author: David Schmeidler
Journal: Proc. Amer. Math. Soc. 34 (1972), 97-101
MSC: Primary 28A55
MathSciNet review: 0293058
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Abstract: It is proved that the values of a set-valued set function, the total variation of which is an atomless finite measure, are conditionally convex.

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  • [1] Z. Artstein, Set-valued measures, Research Program in Game Theory and Mathematical Economics, R.M. #66, May 1971, Department of Mathematics, The Hebrew University of Jerusalem; previous version: R.M. #62, July 1970. MR 0293054 (45:2133)
  • [2] G. Köthe, Topological vector spaces. Vol. I, Die Grundlehren der math. Wissenschaften, Band 159, Springer-Verlag, New York, 1969. MR 40 #1750.
  • [3] D. Schmeidler, ``Convexity and compactness in countably additive correspondences,'' Differential games and related topics (edited by H. W. Kuhn and G. P. Szego), North-Holland, Amsterdam, 1971. See also: Center for Operations Research and Econometrics, D.P. #7019, May 1970, Université Catholique de Louvain. MR 0306442 (46:5568)
  • [4] K. Vind, Edgeworth Allocations in an exchange economy with many traders, Internat. Economic Rev. 5 (1964), 165-177.

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