Convex integral functionals

Transactions of the American Mathematical Society

Volumn 349, Issue 4, 1997, Pages 1421-1436

  Papageorgiou, Nikolaus S ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Conditional expectation; E subdifferential; Multifunction; Normal convex integrand; Singular functional; Souslin space subdifferential; Support function

Indexed keywords

EID: 21744450403     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-97-01478-5     Document Type: Article

References (31)

1. R. Aumann, Markets with a continuum of traders, Econometrica 32 (1964), 39-50. MR 30:2908
2. _, Integrals of set-valued functions, J. Math. Anal. Appl. 12 (1965), 1-12. MR 32:2543
3. R. Aumann and L. Shapley, Values of Nonatomic Games, Princeton Univ. Press, Princeton, 1974.
4. J.-M. Bismut, Intégrales convexes et probabilités, J. Math. Anal. Appl. 42 (1973), 639-673. MR 48:3083
5. N. Bourbaki, Espaces Vectoriels Topologiques, Hermann, Paris, 1966. MR 34:3277
6. C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunction, Springer, Berlin, 1977. MR 57:7169
7. J. Diestel and J. Uhl, Vector Measures, Math Surveys, Vol. 15, AMS, Providence, HI, 1977. MR 56:12216
8. F. Hiai and H. Umegaki, Integrals, conditional expectations and martingales of multivalued functions, 3. Multiv. Anal. 7 (1977), 149-182. MR 58:22463
9. J.-B. Hiriart-Urruty, Thèse d'Etat, Chapter IV, Clermond-Ferrand, France, 1977.
10. _, Lipschitz r-continuity of the approximate subdifferential of a convex function, Math Scand. 47 (1980), 123-134. MR 82c:58007
11. A. loffe and V. Levin, Subdifferentials and convex functions, Trans. Moscow Math. Soc. 26 (1972), 1-72. MR 51:8817
12. A. loffe and V. Tihomirov, The duality of convex functions and extremal problems, Russian Math. Surveys 23 (1968), 53-124. MR 44:5797
13. _, Theory of Extremal Problems, North-Holland, Amsterdam, 1979. MR 80d:49001b
14. H.-A. Klei, Thèse d'Etat, Université de Paris VI, Paris, 1985.
15. N. Komuro, Basic properties of convex functions and convex integrands, Hokkaido Math. Jour. 18 (1989), 1-30. MR 90f:49008
16. P.-J. Laurent, Approximation et Optimisation, Hermann, Paris, 1972. MR 57:6947
17. V. Levin, The Lebesgue decomposition for functionals on the vector-function space Lx, Functional Anal. Appl. 8 (1974), 314-317. MR 57:850
18. _, Convex integral functionals and the theory of lifting, Russian Math. Surveys 30 (1975), 115-178. MR 53:3698
19. N. S. Papageorgiou, Convergence and representation theorems for set-valued random processes, J. Math. Anal. Appl. 150 (1990), 129-145. MR 92a:60117
20. _, Weak convergence of random sets in Banach spaces, J. Math. Anal. Appl. 164 (1992), 571-589. MR 92m:49013
21. R. T. Rockafellar, Integrals which are convex functionals I, Pacific J. Math. 24 (1968), 525539. MR 38:4984
22. _, Integrals which are convex functionals II, Pacific J. Math. 39 (1971), 439-169. MR 46:9710
23. _, Convex integral functionals and duality, in Contributions to Nonlinear Functional Analysis, ed. by E. Zarantonello, Academic Press, New York, 1971, pp. 215-236. MR 52:11693
24. _, Conjugate Duality and Optimization, Reg. Conf. Series in Appl. Math., vol. 16, SIAM, Philadelphia, 1973. MR 51:9811
25. _, Integral functionals, normal integrands and measurable multifunction, in Nonlinear Operators and the Calculus of Variations, ed. by J.-P. Gossez et al., Springer, New York, 1976, pp. 157-207. MR 58:23598
26. _, Convex Analysis, Princeton Univ. Press, Princeton, 1970. MR 43:445
27. R. T. Rockafellar and R. J.-B. Wets, On the interchange of subdifferentiation and conditional expectation for convex functionals, Stochastics 10 (1982), 173-182. MR 83j:49022
28. M.-F. Saint-Beuve, On the extension of von Neumann-Aumann theorem, J. Funct. Anal. 17 (1974), 112-129. MR 51:10564
29. L. Thibault, Espérance conditionelle d'integrandes semicontinus, Ann. Inst. H. Poincare 17 (1981), 337-350. MR 83a:60005
30. M. Valadier, Integration de convexes fermes notamment d'épigraphes et inf-convolution continue, RAIRO 4 (1970), 57-73. MR 43:3881
31. D. Wagner, Survey of measurable selection theorems, SIAM J. Control. Optim. 15 (1977), 859-903. MR 58:6137