Two Generalizations of Komlós' Theorem with Lower Closure-Type Applications

Journal of Convex Analysis

Volumn 3, Issue 1, 1996, Pages 25-44

  Balder, Erik J ^a   Hess, Christian ^b  

^a UTRECHT UNIVERSITY   (Netherlands)

^b UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0345254829     PISSN: 09446532     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (45)

1. 1. Arch. Rational Mech. Anal. 117 (1992) 167-191.
2. Z. Artstein, J.C. Hansen: Convexification in limit laws of random sets in Banach spaces. Ann. Prob. 13 (1985) 307-309.
3. E.J. Balder: A general approach to lower semicontinuity and lower closure in optimal control theory. SIAM J. Control Optim. 22 (1984) 570-598.
4. E.J. Balder: Fatou's lemma in infinite dimensions. J. Math. Anal. Appl. 136 (1988) 450-465.
5. E.J. Balder: Infinite-dimensional extension of a theorem of Komlos. Probab. Th. Rel. Fields 81 (1989) 185-188.
6. E.J. Balder: Unusual applications of a.e. convergence. in: Almost Everywhere Convergence (G.A. Edgar, L. Sucheston, eds.) Academic Press, New York (1989) 31-53.
7. E.J. Balder: New sequential compactness results for spaces of scalarly integrable functions. J. Math. Anal. Appl. 151 (1990) 1-16.
8. E.J. Balder: On uniformly bounded sequences in Orlicz spaces. Bull. Austral. Math. Soc. 41 (1990) 495-502.
9. E.J. Balder: Lectures on Young Measures. Cahiers du Centre de Recherche de Mathématiques de la Décision No. 9517, (1995) CEREMADE, Université Paris IX-Dauphine.
10. E.J. Balder, C. Hess: Fatou's lemma for multifunctions with unbounded values. Math. Oper. Res. 20 (1995) 175-188.
11. P. Billingsley: Probability and Measure. Wiley, New York, 1986.
12. N. Bourbaki: Espaces Vectoriels Topologiques, Chapitres 1 à 5. Masson, Paris, 1981.
13. J. Brooks, R.V. Chacon: Continuity and compactness of measures. Adv. in Math. 37 (1980) 16-26.
14. C. Castaing: Quelques résultats de convergence des suites adaptées. Travaux Sém. Anal. Convexe 17 (1987) 2.1-2.24.
15. C. Castaing: Sur la décomposition de Slaby, applications aux problèmes de convergence en probabilités, economie mathématiques. Théorie du contrôle. Minimisation. Travaux Sém. Anal. Convexe 19 (1989) 3.1-3.35
16. C. Castaing: Méthode de compacité et de décomposition, applications: minimisation, convergence des martingales, lemme de Fatou multivoque. Ann. Mat. Pura Appl. 164 (1993) 51-75.
17. 1(E) et dans l'espace des multifonctions intégrablement bornées, et. minimisation, Ann. Mat. Pura Appl. IV, 140 (1985) 345-364.
18. C. Castaing, P. Clauzure: Lemme de Fatou multivoque. Atti Sem. Mat. Fis. Univ. Modena 39 (1991) 303-320.
19. C. Castaing, M. Valadier: Convex Analysis and Measurable Multifunctions. Lecture Notes in Math. 580, Springer-Verlag, Berlin, 1977.
20. S.D. Chatterji: Les martingales et leurs applications analytiques. in: Ecole d'Eté de Probabilités: Processus Stochastiques. (J.L. Bretagnolle et al., eds.) Lecture Notes in Math. 307 (1973) Springer-Verlag, Berlin, 27-164.
21. J.P.R. Christensen: Topology and Borel Structure. North-Holland, Amsterdam, 1974.
22. A. Costé: La propriété de Radon-Nikodym en intégration multivoque. C.R. Acad. Sci. Paris 280 (1975) 1515-1518.
23. A. Costé: Contribution à la théorie de l'intégration multivoque. Thèse d'Etat, Université Pierre et Marie Curie, Paris. 1977.
24. A. Costé, R. Pallu de La Barrière: Un théorème de Radon-Nikodym pour les multimesures à valeurs fermées localement compactes sans droite. C.R. Acad. Sci. Paris 280 (1975) 255-258.
25. A. Costé, R. Pallu de La Barrière: Radon-Nikodym theorems for set-valued measures whose values are convex and closed. Roczniki PTM Prace Mat. 20 (1978) 283-309.
26. F. De Blasi, J. Myjak: Weak convergence of convex sets in Banach spaces. Arch. Math. 47 (1986) 448-456.
27. C. Dellacherie, P.-A. Meyer: Probabilities and Potential, North-Holland, Amsterdam, 1978.
28. 1 (μ, X). Proc. Amer. Math. Soc. 118 (1993) 447-453.
29. J. Diestel, J.J. Uhl: Vector Measures. AMS Mathematical Surveys 15, Providence, 1977.
30. B. Fuchssteiner, W. Lusky: Convex Cones. Math. Studies 56, North-Holland, Amsterdam, 1981.
31. V.F. Gaposhkin: Convergence and limit theorems for sequences of random variables. Theory Probab. Appl. 17 No. 3 (1972) 379-400.
32. C. Hess: Lemme de Fatou et théorème de la convergence dominée pour des ensembles aléatoires non bornés et des intégrandes. Travaux Sém. Anal. Convexe 16 (1986) 8.1-8.56.
33. C. Hess: Measurability and integrability of the weak upper limit of a sequence of multifunctions. Travaux Sém. Anal. Convexe 10 10.1-10.38 and J. Math. Anal. Appl. 153 (1989) 226-249.
34. C. Hess: Measurability and integrability of the weak upper limit of a sequence of multifunctions. Travaux Sém. Anal. Convexe 10 10.1-10.38 and J. Math. Anal. Appl. 153 (1989) 226-249.
35. C. Hess: Convergence of conditional expectations for unbounded random sets, integrands, and integral functionals. Math. Oper. Res. 16 (1991) 627-649.
36. C. Hess: On multivalued martingales whose values may be unbounded: martingale selectors and Mosco convergence. J. Multivariate Anal. 39 (1991) 175-201.
37. C. Hess: Multivalued strong laws of large numbers in the slice topology. Applicatíon to integrands. Set Valued Anal. 2 (1994) 183-205.
38. F. Hiai: Strong laws of large numbers for multivalued random variables, in: Multifunctions and Integrands (G. Salinetti, ed.) Lecture Notes in Math. 1091, Springer-Verlag, Berlin, 1984.
39. F. Hiai, H. Umegaki: Integrals, conditional expectations, and martingales of multivalued functions. J. Multivariate Anal. 7 (1977) 149-182.
40. 1(E) and Radon-Nikodym theorems for multifunctions. Bull. Sc. Math. 112 (1988) 305-324.
41. J. Komlós: A generalization of a problem of Steinhaus. Acta Math. Acad. Sci. Hungar. 18 (1967) 217-229.
42. J. Lindenstrauss, L. Tzafriri: Classical Banach Spaces I], Springer-Verlag, Berlin, 1977.
43. J.J. Moreau: Fonctionnelles Convexes. Sé]minaire sur les équations aux dérivées partielles, Collè]ge de France, Paris, 1966.
44. R.T. Rockafellar: Level sets and continuity of conjugate functions. Trans. Amer. Math. Soc.] 123 (1966) 46-63.
45. 1, convergence en mesure. Preprint, Université Ibnou Zohr, Agadir, Marocco, 1995.