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A natural supplement of L in the dual of L. Applications

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Bibliography

  1. BISMUT, J-M. Intégrales convexes et probabilités. J. of Math. An. and Appl. 42–3 (1973) 639–673.

    Article  MathSciNet  Google Scholar 

  2. BOURBAKI, N. Intégration Ch. I,II,III,IV 2nd édition.

    Google Scholar 

  3. BOURBAKI, N. Théories spectrales Ch. I, II.

    Google Scholar 

  4. CHOQUET, G. Lectures on Analysis. Benjamin (1969).

    Google Scholar 

  5. DAURES, J-P. Version multivoque du théorème de Doob. Ann. Inst. H-Poincaré IX-2(1973)167–176

    MathSciNet  Google Scholar 

  6. DINCULEANU, N. Vector measures. Pergamon Press (1967).

    Google Scholar 

  7. DIXMIER, J. Sur certains espaces considérés par M.H. Stone. Summa Brasil Math 2 (1951) 151–182.

    MathSciNet  Google Scholar 

  8. DUBOVITSKII, A. Ya. MILIUTIN, A.A. Necessary condition for a weak extremum in problems of optimal control with mixed constraints of inequality type. Zh. Vychisl. Mat. i Mat. Fys. 8(1968) 725–779.

    MATH  Google Scholar 

  9. DUNFORD, N. SCHWARTZ, J.T. Linear operators. Part I. John Wiley (1964).

    Google Scholar 

  10. FHIMA, G. Applications intégrales et intégrandes convexes. Décomposition du dual de L E . Thèse de 3ème cycle Paris (1974).

    Google Scholar 

  11. HIRIART-URRUTY, J-B. Etude de quelques propriétés de la fonctionnelle moyenne et de l'inf-convolution continue en analyse convexe stochastique. C.R. Ac. Sc. 280 (1975) 129–132.

    MATH  Google Scholar 

  12. HUFF, R.E. The Yosida-Hewitt decomposition as an ergodic theorem in Vector and Operator Valued Measures edited by Tuckerand Maynard Academic Press. 1973 p.133–139.

    Google Scholar 

  13. IOFFE, A.D. LEVIN, V.L. Subdifferentials of convex functions. Trudy Mosk. Mat. Ob. 26 (1972) 3–73.

    MathSciNet  MATH  Google Scholar 

  14. IOFFE, A.D. TIHOMIROV, V.M. Minimisation of an integral functional. Funkt. an i priloj 3–3 (1969) 61–70.

    MathSciNet  Google Scholar 

  15. IONESCU TULCEA, A. and C. Topics in the theory of lifting. Springer Verlag (1969)

    Google Scholar 

  16. LEVIN, V.L. Lebesgue decomposition of functionals on L X . Funkt. Anal. 8–4 (1974) 48–53.

    Google Scholar 

  17. LEVIN, V.L. Convex integral functionals and theory of lifting. Uspehi Mat. Nauk. XXX-2 (1975) 115–178

    Google Scholar 

  18. NEVEU, J. Bases mathématiques du calcul des probabilités. Masson (1964).

    Google Scholar 

  19. NEVEU, J. Convergence presque sûre de martingales multivoques. Annales Inst. H. Poincaré VIII-1 (1972) 1–7.

    MathSciNet  Google Scholar 

  20. PALLU DE LA BARRIERE, R. Etudes de quelques espaces liés à l'intégration multivoque C.R. Acad. Sc. 278 (1974) 1491–1494.

    MathSciNet  MATH  Google Scholar 

  21. PERESSINI, A.L. Ordered topological vector spaces Harper Row (1967).

    Google Scholar 

  22. ROCKAFELLAR, R.T. Convex integral functionals and duality. Contribution to non linear functional analysis. Academic Press (1971) p. 215–236.

    Google Scholar 

  23. ROCKAFELLAR, R.T. Decomposition in L Y * for infinite-dimensional Y. Unpublished.

    Google Scholar 

  24. ROCKAFELLAR, R.T. Integrals which are convex functionals II. Pacific J. Math. 39–2(1971) 439–469.

    Article  MathSciNet  Google Scholar 

  25. SCALORA, F.S. Abstract martingale convergence theorems. Pacific J. Math. 11(1961)347–374.

    Article  MathSciNet  MATH  Google Scholar 

  26. VALADIER, M. Intégration de convexes fermés, notamment d'épigraphes. RIRO R2 (1970) 57–73.

    MathSciNet  Google Scholar 

  27. VALADIER, M. Une propriété du dual de L E′ . Séminaire d'Analyse Convexe. Montpellier (1972).

    Google Scholar 

  28. VALADIER, M. Espérance conditionnelle d'un convexe fermé aléatoire. Comptes Rendus Ac. Sc. 273 (1971) 1265–1267 (see also Séminaire d'Analyse Convexe, Montpellier, 1972 exposé no1)

    MathSciNet  MATH  Google Scholar 

  29. VAN CUTSEM, B. Eléments aléatoires à valeurs convexes compactes. Thèse Grenoble 1971.

    Google Scholar 

  30. VULIKH, B.Z. Introduction to the theory of partially ordered spaces Noordhoff (1967).

    Google Scholar 

  31. YOSIDA, K. HEWITT, E. Finitely additive measures. Trans. A.M.S. 72(1952)46–66.

    Article  MathSciNet  MATH  Google Scholar 

  32. ZAANEN, A.C. Integration 2nd édition. North Holland (1967).

    Google Scholar 

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Castaing, C., Valadier, M. (1977). A natural supplement of L in the dual of L. Applications. In: Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics, vol 580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087693

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  • DOI: https://doi.org/10.1007/BFb0087693

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  • Print ISBN: 978-3-540-08144-9

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