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
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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
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