Keywords
- Convex Compact
- Radon Measure
- Vector Measure
- Positive Radon Measure
- Empty Convex
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Bibliography of Chapter IV
ALFSEN, E.M.-Compact convex sets and boundary integrals. Springer-Verlag. Berlin Heidelberg New York 1971.
ARKIN, V.I.-LEVIN, V.L.-Convexity of values of vector integrals theorems on measurable choices and variationals problems. Russian Math. Surveys 27, 21–85 (1972).
BENAMARA, M.-Sections extrémales d'une multi-application. C.R. Acad. Sc. Paris 278, 1249–1252 (1974).
Points extrémaux multi-applications et fonctionnelles intégrales. Thèse de 3o cycle, Grenoble (1975).
BERGE, C.-Espaces topologiques. Fonctions multivoques. Dunod 1958.
BLACKWELL, D.-The range of certain vector integrals. Proc. Amer. Math. Society 2, 390–395 (1951).
BOURBAKI, N.-Topologie générale. Chapitre 9. 2ème édition. Hermann Paris 1958.
-Intégration sur les espaces topologiques séparés. Chapitre 9 Hermann Paris 1969.
CASTAING, Ch.-Sur les multi-applications mesurables. Revue d'Informatique et de Recherche opérationnelle 1, 91–126 (1967).
Sur la mesurabilité du profil d'un ensemble convexe compact variant de façon mesurable. Collège Scientifique Universitaire Perpignan (1968). Polycopié.
-Sur une nouvelle extension du théorème de Ljapunov. C.R. Acad. Sc. Paris 264, 333–336 (1967).
-Application d'un théorème de compacité à un résultat de désintégration des mesures. C.R. Acad. Sc. Paris 270, 1732–1735 (1970).
CHOQUET, G.-MEYER, P.A.-Existence et unicité des représentations intégrales dans les convexes compacts quelconques. Ann. Inst. Fourier (Grenoble) 13, 139–154 (1963).
DUNFORD, N.-SCHWARTZ, J.T.-Linear operators. Part. I. Interscience 1964.
DVORETZKY, A.-WALD, A.-WOLFOWITZ, J.-Relations among certain ranges of vector measures. Pacific J. Math. 1, 59–74 (1951).
GODET-THOBIE, C.-Sur les multimesures de transition. C.R. Acad. Sc. Paris 278, 1367–1369 (1974) et exposé no 5, Séminaire d'Analyse convexe Montpellier (1974).
GHOUILA HOURI, A.-Sur la généralisation de la notion de commande d'un système guidable. Revue d'Informatique et de recherche opérationnelle 4, 7–32 (1967).
HALMOS, P.R.-The range of a vector measure. Bull. Amer. Math. Soc. 54, 416–421 (1948).
KARLIN, S.-On extreme points of vector functions. Proc. Amer. Math. Society 4, 603–610 (1953).
KARLIN, S.-STUDDEN, W.J.-Tchebycheff systems; with applications in Analysis and Statistics. John Wiley 1966.
KELLERER, H.G.-Bemerkung zn einen satz von H. Richter. Archiv. der Math. 15, 204–207 (1964).
KINGMAN, J.F.C.-ROBERTSON, A.P.-On a theorem of Liapounoff, J. of London Math. Soc. 43, 347–351 (1968).
LINDENSTRAUSS, J.-A shorf proof of Liapounoff's convexity theorem. J. of Math. and Mechanics 15, 971–972 (1966).
LJAPUNOV, A.-Sur les fonctions-vecteurs complètement additives. Bull. Acad. Sci. URSS sér. Math. 4, 465–478 (1940).
MEYER, P.A.-Probabilités et Potentiel. Hermann 1966.
NEVEU, J.-Bases mathématiques du calcul des probabilités. Masson 1964.
OLECH, C.-Extremal solutions of a control system. J. Differential equations 2, 74–101 (1966).
SAINTE-BEUVE, M.F.-On the extension of Von Neumann-Aumann's theorem. J. Functional Analysis 17, 112–129 (1974).
STRASSEN, V.-The existence of probability measures with given marginals. Ann. Math. Stat. 36, 423–439 (1965).
VALADIER, M.-Contribution à l'analyse convexe. Thèse Faculté des Sciences (Paris) (1970).
WARGA, J.-Optimal control of Differential and Functional Equations, Academic Press, New York 1972.
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Castaing, C., Valadier, M. (1977). Topological property of the profile of a measurable multifunction with compact convex values. In: Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics, vol 580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087689
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DOI: https://doi.org/10.1007/BFb0087689
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