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Dans un espace de Banach reticulé solide, la propriété de Radon-Nikodým et celle de Kreĭn-Milman sont équivalentes


Authors: Jean Bourgain and Michel Talagrand
Journal: Proc. Amer. Math. Soc. 81 (1981), 93-96
MSC: Primary 46B22; Secondary 46B30
DOI: https://doi.org/10.1090/S0002-9939-1981-0589144-X
MathSciNet review: 589144
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Abstract: Un espace de Banach réticulé solide possède la propriété de Radon-Nikodým si et seulement si tout convexe fermé borné est enveloppe convexe fermée de ses points extrémaux.


References [Enhancements On Off] (What's this?)

  • [1] J. Bourgain, A geometric characterization of Radon-Nikodym property in Banach spaces, Compositio Math. 36 (1978), 3-6. MR 515034 (80h:46018)
  • [2] J. Diestel, Geometry of Banach spaces-Selected topics, Lecture Notes in Math., vol. 485, Springer-Verlag, Berlin and New York, 1975. MR 0461094 (57:1079)
  • [3] N. Ghoussoub, Riesz-space valued measures and processes, J. Multivariate Analysis (à paraitre).
  • [4] N. Ghoussoub and M. Talagrand, Order dentability in Banach lattices, Math. Ann. (à paraitre).
  • [5] H. H. Shaffer, Banach lattices and positive operators, Springer-Verlag, Berlin and New York, 1974. MR 0423039 (54:11023)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0589144-X
Keywords: Banach lattice, Radon-Nikodým, extreme points
Article copyright: © Copyright 1981 American Mathematical Society

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