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Radon-Nikodym theorems for set-valued measures. (English) Zbl 0384.28006

MSC:
28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
28A25 Integration with respect to measures and other set functions
28A15 Abstract differentiation theory, differentiation of set functions
46B22 Radon-Nikodým, Kreĭn-Milman and related properties
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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[1] Amir, D.; Lindenstrauss, J., The structure of weakly compact sets in Banach spaces, Ann. of math., 88, 35-46, (1968) · Zbl 0164.14903
[2] Artstein, Z., Set-valued measures, Trans. amer. math. soc., 165, 103-125, (1972) · Zbl 0237.28008
[3] Aumann, R.J., Integrals of set-valued functions, J. math. anal. appl., 12, 1-12, (1965) · Zbl 0163.06301
[4] Bartle, R.G.; Dunford, N.; Schwartz, J., Weak compactness and vector measures, Canad. J. math., 7, 289-305, (1955) · Zbl 0068.09301
[5] Castaing, C., Sur LES multi-applications mesurables, Rev. fr. inform. recherche opér., 1, 91-126, (1967) · Zbl 0153.08501
[6] Castaing, C., Le théorème de Dunford-Pettis généralisé, C. R. acad. sci. Paris Sér. A, 268, 327-329, (1969) · Zbl 0184.40203
[7] Costé, A., Sur LES multimesures à valeurs fermées bornées d’un espace de Banach, C. R. acad. sci. Paris Sér. A, 280, 567-570, (1975) · Zbl 0295.46069
[8] Davis, W.J.; Phelps, R.R., The Radon-Nikodym property and dentable sets in Banach spaces, (), 119-122 · Zbl 0298.46046
[9] Debreu, G., Integration of correspondences, (), 351-372, Part I · Zbl 0211.52803
[10] Debreu, G.; Schmeidler, D., The Radon-nikodým derivative of a correspondence, (), 41-56
[11] Diestel, J.; Uhl, J.J., The Radon-Nikodym theorem for Banach space valued measures, Rocky mt. J. math., 6, 1-46, (1976) · Zbl 0339.46031
[12] Dunford, N.; Pettis, B.J., Linear operations on summable functions, Trans. amer. math. soc., 47, 323-392, (1940) · Zbl 0023.32902
[13] Dunford, N.; Schwartz, J.T., ()
[14] Godet-Thobie, C., Sélections de multimesures. application à un théorème de Radon-Nikodym multivoque, C. R. acad. sci. Paris Sér. A, 279, 603-606, (1974) · Zbl 0307.28013
[15] Hausdorff, F., Set theory, (1957), Chelsea, New York (Transl. from German) · Zbl 0060.12401
[16] Hiai, F.; Umegaki, H., Integrals, conditional expectations, and martingales of multivalued functions, J. multivariate anal., 7, 149-182, (1977) · Zbl 0368.60006
[17] Himmelberg, C.J., Measurable relations, Fund. math., 87, 53-72, (1975) · Zbl 0296.28003
[18] Huff, R.E., Dentability and the Radon-nikodým property, Duke math. J., 41, 111-114, (1974) · Zbl 0285.46037
[19] Hukuhara, M., Intégration des applications mesurables dont la valeur est un compact convexe, Funkcial. ekvac., 10, 205-223, (1967) · Zbl 0161.24701
[20] Klee, V.L., Convex sets in linear spaces, II, Duke math. J., 18, 875-883, (1951) · Zbl 0044.11201
[21] Maynard, H.B., A geometrical characterization of Banach spaces with the Radon-Nikodym property, Trans. amer. math. soc., 185, 493-500, (1973) · Zbl 0278.46040
[22] Phelps, R.R., Dentability and extreme points in Banach spaces, J. functional analysis, 16, 78-90, (1974) · Zbl 0287.46026
[23] Phillips, R.S., On weakly compact subsets of a Banach space, Amer. J. math., 65, 108-136, (1943) · Zbl 0063.06212
[24] Rådström, H., An embedding theorem for spaces of convex sets, (), 165-169 · Zbl 0046.33304
[25] Rieffel, M.A., Dentable subsets of Banach spaces, with application to a Radon-Nikodym theorem, (), 71-77 · Zbl 0213.13703
[26] Rieffel, M.A., The Radon-Nikodym theorem for the Bochner integral, Trans. amer. math. soc., 131, 466-487, (1968) · Zbl 0169.46803
[27] Rockafellar, R.T., Measurable dependence of convex sets and functions on parameters, J. math. anal. appl., 28, 4-25, (1969) · Zbl 0202.33804
[28] Troyanski, S.L., On locally uniformly convex and differentiable norms in certain non-separable Banach spaces, Studia math., 37, 173-180, (1971) · Zbl 0214.12701
[29] Uhl, J.J., The range of a vector-valued measure, (), 158-163 · Zbl 0182.46903
[30] Costé, A., La propriété de Radon-Nikodym en intégration multivoque, C. R. acad. sci. Paris Sér. A, 280, 1515-1518, (1975) · Zbl 0313.28007
[31] Costé, A.; Pallu de La Barrière, R., Un théorème de Radon-Nikodym pour LES multimesures à valeurs convexes fermées localement compactes sans droite, C. R. acad. sci. Paris Sér. A, 280, 255-258, (1975) · Zbl 0299.46041
[32] Doob, J.L., ()
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