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A Choquet theorem for general subspaces of vector-valued functions

Published online by Cambridge University Press:  24 October 2008

Paulette Saab  and
Michel Talagrand
Paulette Saab
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A.
Michel Talagrand
Affiliation:
Equipe d' Analyse, Université Paris VI, 75230 Paris Cedex 05, France
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Extract

Let X be a compact Hausdorff space, let E be a (real or complex) Banach space, and let C(X, E) stand for the Banach space of all continuous E-valued functions defined on X under the supremum norm. If A is an arbitrary linear subspace of C(X, E), then it is shown that each bounded linear functional l on A can be represented by a boundary E*-valued vector measure μ on X that has the same norm as l. This result constitutes an extension to vector-valued functions of the so-called analytic version of Choquet's integral representation theorem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 2 , September 1985 , pp. 323 - 326
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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