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

 

Points extrémaux dans le dual de $ L\sp{1}(\mu ,\,E)$


Author: Michel Talagrand
Journal: Proc. Amer. Math. Soc. 91 (1984), 265-269
MSC: Primary 46E40; Secondary 46A55, 46E30
MathSciNet review: 740183
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Abstract: The dual of $ {L^1}(\mu ,E)$ is the space of bounded weak* scalarly measurable functions $ f:\Omega \to {E^ * }$. We show that $ f$ is extremal in the unit ball of $ {L^1}{(\mu ,E)^ * }$ if and only if the probability it induces on the unit ball of $ {E^*}$ is maximal for the Choquet order.


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

  • [1] G. Choquet, Lecture on analysis, Benjamin, New York, 1969.
  • [2] A. and I. Ionescu-Tulcea, Topics in the theory of lifting, Springer-Verlag, Berlin and New York, 1979.
  • [3] Robert R. Phelps, Lectures on Choquet’s theorem, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0193470 (33 #1690)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0740183-8
PII: S 0002-9939(1984)0740183-8
Article copyright: © Copyright 1984 American Mathematical Society