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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


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
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 the Radon-Nikodým property in Banach spaces, Compositio Math. 36 (1978), no. 1, 3–6. MR 515034 (80h:46018)
  • [2] Joseph Diestel, Geometry of Banach spaces—selected topics, Lecture Notes in Mathematics, Vol. 485, Springer-Verlag, Berlin-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] Helmut H. Schaefer, Banach lattices and positive operators, Springer-Verlag, New York-Heidelberg, 1974. Die Grundlehren der mathematischen Wissenschaften, Band 215. MR 0423039 (54 #11023)

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Additional Information

PII: S 0002-9939(1981)0589144-X
Keywords: Banach lattice, Radon-Nikodým, extreme points
Article copyright: © Copyright 1981 American Mathematical Society

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