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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Points extrémaux dans le dual de $L^{1}(\mu , E)$
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by Michel Talagrand PDF
Proc. Amer. Math. Soc. 91 (1984), 265-269 Request permission

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
    G. Choquet, Lecture on analysis, Benjamin, New York, 1969. A. and I. Ionescu-Tulcea, Topics in the theory of lifting, Springer-Verlag, Berlin and New York, 1979.
  • Robert R. Phelps, Lectures on Choquet’s theorem, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0193470
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 91 (1984), 265-269
  • MSC: Primary 46E40; Secondary 46A55, 46E30
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0740183-8
  • MathSciNet review: 740183