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On the Choquet representation theorem

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References

  1. E. Alfsen. “Compact Convex Sets and Boundary Integrals”, Springer-Verlag, Berlin, New York, 1971.

    Book  MATH  Google Scholar 

  2. L. Asimov and A.J. Ellis. “Convexity theory and its applications in functional analysis”, Academic Press, London, New York, 1980.

    Google Scholar 

  3. J. Baire and R. Fourneau. “Etude Géométrique des Espaces Vectoriels — une Introduction”, Lecture Notes in Mathematics, 489 Springer-Verlag, Berlin, New York, 1970.

    Google Scholar 

  4. J. Baire and R. Fourneau. “Etude Géométrique des Espaces Vectoriels II — Polyédres et Polytopes Convexes”, Lecture Notes in Mathematics, 802 Springer-Verlag, Berlin, New York, 1980.

    Google Scholar 

  5. E. Bishop and K. de Leeuw. The representation of linear functionals by measures on sets of extreme points, Ann. Inst. Fourier (Grenoble), 9 (1959), 305–331.

    Article  MATH  MathSciNet  Google Scholar 

  6. F.F. Bonsall. On the representation of points of a convex set, J. London Math. Soc., 38 (1963), 332–334.

    Article  MATH  MathSciNet  Google Scholar 

  7. V. Borovikov. On the intersection of a sequence of simplices, (Russian), Uspehi Mat. Nauk., 7 (6) (1952), 179–180.

    MathSciNet  Google Scholar 

  8. G. Choquet. Unicité des représentations intégrales au moyen des points extrémaux dans les cônes convexes réticulés, C.R. Acad. Sci. Paris, 243 (1956), 555–557.

    MATH  MathSciNet  Google Scholar 

  9. G. Choquet. Existence des représentations intégrales au moyen des points extrémaux dans les cônes convexes, C.R. Acad. Sci. Paris, 243 (1956), 699–702.

    MATH  MathSciNet  Google Scholar 

  10. G. Choquet. Existence et unicité des representations intégrales au moyen des points extrémaux dans les cônes convexes, Séminaire Bourbaki, (Dec. 1956), 133, 15 pp.

    Google Scholar 

  11. G.A. Edgar. A noncompact Choquet theorem, Proc. Amer. Math. Soc., 49 (1975), 354–358.

    Article  MATH  MathSciNet  Google Scholar 

  12. H.G. Eggleston, B. Grünbaum and V. Klee. Some semicontinuity theorems for convex polytopes and cell-complexes, Comm. Math. Helv., 39 (1964), 165–188.

    Article  MATH  Google Scholar 

  13. A. Goullet de Rugy, “frGéométrie des Simplexes”, Centre de Documentation Universitaire, Paris, (1968), 84 pp.

    Google Scholar 

  14. N. Ghoussoub and B. Maurey. H δ-embeddings in Hilbert space and optimization on G δ-sets, Memoirs Amer. Math. Soc., 349 (1986).

    Google Scholar 

  15. M. Hervé. Sur les représentations intégrales a l'aide des points extrémaux dans un ensemble compact convexe métrisable, C.R. Acad. Sci. Paris, 253 (1961), 366–368.

    MATH  MathSciNet  Google Scholar 

  16. D.G. Kendall. Simplexes and vector lattices, J. London Math. Soc., 37 (1962), 365–371.

    Article  MATH  MathSciNet  Google Scholar 

  17. R.R. Phelps. “Lectures on Choquet's Theorem”, Van Nostrand, Princeton, 1966.

    MATH  Google Scholar 

  18. R.R. Phelps. Integral representations for elements of convex sets, in “Studies in Functional Analysis”, MAA Studies in Math, 21, 1980.

    Google Scholar 

  19. C.A. Rogers and G.C. Shephard. The difference body of a convex body, Arch. Math., 8 (1957), 220–233.

    Article  MATH  MathSciNet  Google Scholar 

  20. H.P. Rosenthal. Geometric properties related to the Radon-Nikodým property, Seminaire d'Initiation a l'Analyse, University of Paris VI, 20e Année, (1980–81), No.22, 14pp.

    Google Scholar 

  21. H.P. Rosenthal. On the structure of non-dentable closed bounded convex sets, Advances in Math., (to appear).

    Google Scholar 

  22. H.P. Rosenthal. L 1-convexity, Longhorn Notes, this issue, 156–174.

    Google Scholar 

  23. H.P. Rosenthal. Martingale proofs of a general integral representation theorem, (to appear).

    Google Scholar 

  24. J. Saint Raymond. Représentation intégrale dans certain convexes, Sem. Choquet, 14e Année, University of Paris VI, (1974), No.2, 11pp.

    Google Scholar 

  25. H.H. Schaefer, “Banach Lattices and Positive Operators”, Springer-Verlag, Berlin, New York, 1970.

    Google Scholar 

  26. G. Winkler. “Choquet order and simplices: with applications in probabilistic models”, Lecture Notes in Mathematics, 1145, Springer-Verlag, Berlin, New York, 1985.

    MATH  Google Scholar 

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© 1988 Springer-Verlag Berlin Heidelberg

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Rosenthal, H. (1988). On the Choquet representation theorem. In: Odell, E.W., Rosenthal, H.P. (eds) Functional Analysis. Lecture Notes in Mathematics, vol 1332. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081608

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  • DOI: https://doi.org/10.1007/BFb0081608

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  • Print ISBN: 978-3-540-50018-6

  • Online ISBN: 978-3-540-45892-0

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