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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Compacité extrémale


Authors: Jean Bourgain and Michel Talagrand
Journal: Proc. Amer. Math. Soc. 80 (1980), 68-70
MSC: Primary 46B10; Secondary 46A50
DOI: https://doi.org/10.1090/S0002-9939-1980-0574510-8
MathSciNet review: 574510
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Abstract: Un ensemble borné d'un espace de Banach E est faiblement compact dès qu'il est compact pour la topologie de la convergence simple sur les points extrêmaux de la boule unité du dual de E.


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

  • [1] G. Choquet, Lectures on analysis, Benjamin, New York, 1969.
  • [2] J. Bourgain, D. H. Fremlin, and M. Talagrand, Pointwise compact sets of Baire-measurable functions, Amer. J. Math. 100 (1978), no. 4, 845–886. MR 509077, https://doi.org/10.2307/2373913
  • [3] K. Kuratowski, Topology. Vol. I, New edition, revised and augmented. Translated from the French by J. Jaworowski, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1966. MR 0217751
  • [4] M. Talagrand, Espaces de Banach faiblement $ \mathcal{H}$-analytiques, Ann. of Math. (a paraître)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0574510-8
Keywords: Extreme point, integral representation
Article copyright: © Copyright 1980 American Mathematical Society