On set correspondences into uniformly convex Banach spaces
Author:
David Schmeidler
Journal:
Proc. Amer. Math. Soc. 34 (1972), 97-101
MSC:
Primary 28A55
DOI:
https://doi.org/10.1090/S0002-9939-1972-0293058-7
MathSciNet review:
0293058
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Abstract | References | Similar Articles | Additional Information
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.
- [1] Zvi Artstein, Set-valued measures, Trans. Amer. Math. Soc. 165 (1972), 103–125. MR 293054, https://doi.org/10.1090/S0002-9947-1972-0293054-4
- [2] G. Köthe, Topological vector spaces. Vol. I, Die Grundlehren der math. Wissenschaften, Band 159, Springer-Verlag, New York, 1969. MR 40 #1750.
- [3] David Schmeidler, Convexity and compactness in countably additive correspondences, Differential Games and Related Topics (Proc. Internat. Summer School, Varenna, 1970) North-Holland, Amsterdam, 1971, pp. 235–242. MR 0306442
- [4] K. Vind, Edgeworth Allocations in an exchange economy with many traders, Internat. Economic Rev. 5 (1964), 165-177.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1972-0293058-7
Article copyright:
© Copyright 1972
American Mathematical Society
