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.
- Zvi Artstein, Set-valued measures, Trans. Amer. Math. Soc. 165 (1972), 103–125. MR 293054, DOI 10.1090/S0002-9947-1972-0293054-4 G. Köthe, Topological vector spaces. Vol. I, Die Grundlehren der math. Wissenschaften, Band 159, Springer-Verlag, New York, 1969. MR 40 #1750.
- 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 K. Vind, Edgeworth Allocations in an exchange economy with many traders, Internat. Economic Rev. 5 (1964), 165-177.
- © Copyright 1972 American Mathematical Society
- 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