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Integrals, conditional expectations, and martingales of multivalued functions. (English) Zbl 0368.60006


MSC:

60B05 Probability measures on topological spaces
28B05 Vector-valued set functions, measures and integrals
Full Text: DOI

References:

[1] Aumann, R. J., Integrals of set-valued functions, J. Math. Anal. Appl., 12, 1-12 (1965) · Zbl 0163.06301
[2] Castaing, C., Sur les multi-applications mesurables, Rev. Fr. Inf. Recher. Oper., 1, 91-126 (1967) · Zbl 0153.08501
[3] Castaing, C., Le théorème de Dunford-Pettis généralisé, (C. R. Acad. Sci. (Paris) Sér. A, 268 (1969), Secrétariat des Mathématiques, Université de Montpellier), 327-329, See also Publication No. 43 · Zbl 0184.40203
[4] Castaing, C., Un théorème de compacité faible dans \(LE^1\), Applications: sous gradients et équations différentielles multivoques dans les espaces de Banach réflexifs non nécessairement séparables, (Publication No. 44 (1969), Secrétariat des Mathématiques, Université de Montpellier) · Zbl 0217.09203
[5] Chatterji, S. D., Martingales of Banach-valued random variables, Bull. Amer. Math. Soc., 66, 395-398 (1960) · Zbl 0102.13601
[6] Chatterji, S. D., A note on the convergence of Banach-space valued martingales, Math. Ann., 153, 142-149 (1964) · Zbl 0125.36703
[7] Chatterji, S. D., Martingale convergence and the Radon-Nikodym theorem in Banach spaces, Math. Scand., 22, 21-41 (1968) · Zbl 0175.14503
[8] Debreu, G., Integration of correspondences, (Proc. Fifth Berkeley Sympos. on Math. Statist. and Probability, Vol. II (1966)), 351-372, Part I · Zbl 0211.52803
[9] Dinculeanu, N., (Vector Measures (1967), Pergamon Press: Pergamon Press London)
[10] Dinculeanu, N., Conditional expectations for general measure spaces, J. Multivariate Anal., 1, 347-364 (1971) · Zbl 0238.60004
[11] Dinculeanu, N.; Rao, M. M., Contractive projections and conditional expectations, J. Multivariate Anal., 2, 362-381 (1972) · Zbl 0251.47011
[12] Dunford, N.; Schwartz, J. T., (Linear Operators, Part I: General Theory (1958), Interscience: Interscience New York) · Zbl 0084.10402
[13] Hausdorff, F., Set Theory (1957), Chelsea, New York (Transl. from German) · Zbl 0060.12401
[14] Himmelberg, C. J., Measurable relations, Fund. Math., 87, 53-72 (1975) · Zbl 0296.28003
[15] Himmelberg, C. J.; Van-Vleck, F. S., Some selection theorems for measurable functions, Canad. J. Math., 21, 394-399 (1969) · Zbl 0202.33803
[16] Hukuhara, M., Intégration des applications mesurables dont la valeur est un compact convexe, Funkcial. Ekvac., 10, 205-223 (1967) · Zbl 0161.24701
[17] Jacobs, M. Q., Measurable multivalued mappings and Lusin’s theorem, Trans. Amer. Math. Soc., 134, 471-481 (1968) · Zbl 0169.06801
[18] Kuratowski, K., (Topology, Vol. I (1966), Academic Press: Academic Press New York-London-Warszawa), (Transl. from French) · Zbl 0158.40802
[19] Kuratowski, K.; Ryll-Nardzewski, C., A general theorem on selectors, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 13, 397-403 (1965) · Zbl 0152.21403
[20] Olech, C., A note concerning set-valued measurable functions, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 13, 317-321 (1965) · Zbl 0145.28302
[21] Pliś, A., Remark on measurable set-valued functions, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 9, 857-859 (1961) · Zbl 0101.04303
[22] Rådström, H., An embedding theorem for spaces of convex sets, (Proc. Amer. Math. Soc., 3 (1952)), 165-169 · Zbl 0046.33304
[23] Rao, M. M., Linear operators, tensor products, and contractive projections in function spaces, Studia Math., 38, 131-186 (1970) · Zbl 0224.46034
[24] Rao, M. M., Conditional measures and operators, J. Multivariate Anal., 5, 330-413 (1975) · Zbl 0327.60005
[25] Rockafellar, R. T., Integrals which are convex functions, Pacific J. Math., 24, 525-539 (1968) · Zbl 0159.43804
[26] Rockafellar, R. T., Measurable dependence of convex sets and functions on parameters, J. Math. Anal. Appl., 28, 4-25 (1969) · Zbl 0202.33804
[27] Rockafellar, R. T., Convex integral functionals and duality, (Zarantonello, E., Contributions to Nonlinear Functional Analysis (1971), Academic Press: Academic Press New York), 215-236 · Zbl 0326.49008
[28] Scalora, F. S., Abstract martingale convergence theorems, Pacific J. Math., 11, 347-374 (1961) · Zbl 0114.07702
[29] Uhl, J. J., Applications of Radon-Nikodým theorems to martingale convergence, Trans. Amer. Math. Soc., 145, 271-285 (1969) · Zbl 0211.21903
[30] Uhl, J. J., The range of a vector-valued measure, (Proc. Amer. Math. Soc., 23 (1969)), 158-163 · Zbl 0182.46903
[31] Umegaki, H., Conditional expectation in an operator algebra, Tôhoku Math. J., 6, 177-181 (1954) · Zbl 0058.10503
[32] Umegaki, H., Conditional expectation in an operator algebra, II, Tôhoku Math. J., 8, 86-100 (1956) · Zbl 0072.12501
[33] Umegaki, H.; Bharucha-Reid, A. T., Banach space-valued random variables and tensor products of Banach spaces, J. Math. Anal. Appl., 31, 49-67 (1970) · Zbl 0292.60008
[34] Artstein, Z., Set-valued measures, Trans. Amer. Math. Soc., 165, 103-125 (1972) · Zbl 0237.28008
[35] Godet-Thobie, C., On transition multi-measures, (Exposé No. 3 (1975), Caen. Univ. de Breś), 12 · Zbl 0359.28009
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