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Abstrakty
In [15] Topsoe characterizes the narrowly compact subsets of measures in general situations. The basie tool used is extension of a content to a measure. In this paper we generalize to tight set-valued map these theorems of extension [15, Theorem l, p. 198; Theorem 2 and 3, p. 201]. In our next papers we shall apply these results to the study of compactness in space of set-valued measures.
Wydawca
Rocznik
Tom
Strony
251--259
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
- University of Lome, Faculty of Sciences, Departement of Mathematics, P. Box 1515 Lome, Togo
Bibliografia
- [1] Z. Artstein, Set-valued measures, Trans. Amer. Math. Soc., 165 (1972) 103-125.
- [2] N. Bourbaki, Integration, Chapter IX, ed.: Hermann, Paris 1969.
- [3] J. K. Brooks, An integration theory for set-valued measures I, II, Bull. Soc. Roy. Sci. Liège, (1968) 312-319 and 375-380.
- [4] A. Costé, R. Pallu De La Barrière, Radon-Nikodým theorems for set-valued measures whose values are convex and closed, Comment. Math. Prace Mat., XX (1978) 283-309.
- [5] G. Debreu, Integration of correspondance, in: Proc. Fifth Berkeley Sympos. Math. Statist, and Probability, Berkeley and Los Angeles, California Univ. Press, Vol. 2, Part 1 (1967) 351-372.
- [6] G. Debreu, D. Schmeidler, The Radon-Nikodým derivative of a correspondance, in: Proc. Sixth. Berkeley Sympos. Math. Statist, and Probability, Berkeley and Los Angeles, California Univ. Press, 2 (1972) 41-56.
- [7] L. Drewnowski, Additive and countably additive correspondance, Comment. Math. Prace Mat., XIX (1976) 25-54.
- [8] Ch. Godet-Thobie, Sur les sélections de multimesures généralisées, C.R. Acad. Sci. Paris Sér. I Math., 271 (1970) 153-156.
- [9] L. Hörmander, Sur la fonction d’appui des ensembles convexes dans un espace localement convexe, Ark. Mat., 3 (12) (1954) 181-186.
- [10] J. Kisyński, On the generation of tight measures, Studia Math., 30 (1968) 141-152.
- [11] J. J. Moreau, Fonctionnelles convexes, in: Séminaires sur les équations aux dérivées partielles II, Collège de Prance, (1966-67) 1-108.
- [12] R. Pallu De La Barriere, Convex analysis, vector and set-valued measures, I-II-III, Publ. Math. Univ. Pierre et Marie Curie, no. 33, pp. 1-23, 1-32, 1-28.
- [13] D. Schmeidler, Convexity and compactness in countably additive correspondances, in: Differential games and related topics, North-Holland. Amsterdam London (1971) 235-242.
- [14] D. Schmeidler, On set correspondance into uniformly convex Banach spaces, Proc. Amer. Math. Soc., 34 (1972) 97-101.
- [15] F. Topsøe, Compactness in spaces of measures. Studia Math., 36 (1970) 195-212.
- [16] M. Valadier, Multi-applications mesurables à valeurs compactes, J. Math. Pures Appl., 50 (1971) 265-297.
- [17] K. Vind, Edgeworth, Allocations in an exchange economy with many traders, Internat. Econom. Rev., 5 (1964) 165-177.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BAT5-0001-0066