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Sur les mesures coniques localisables

Part of: Topological linear spaces and related structures

Published online by Cambridge University Press:  09 April 2009

Richard Becker
Richard Becker
Affiliation:
Université Paris VI Equipe d'Analyse, E.R.A 294 4 Place Jussieu 75230, Paris, France
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Abstract

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Let X be a weakly complete proper cone, contained in an Hausdorff locally convex space E, with continuous dual E′. A positive linear form on the Risz space of functions on X generated by E′ is called a conical measure on X. Let M+ (X) be the set of all conical measures on X. G. Choquet asked the question: when is every conical measure on X given by a Radon measure on (X\0)? Let L be the class of such X. In this paper we show that the fact that X ∈ L only depends, in some sense, on the cofinal subsets of the space E′|x ordered by the order of functions on X. We derive that X ∈ L is equivalent to M+ (M) ∈ L. We show that is closed under denumerable products.

MSC classification

Secondary: 46A55: Convex sets in topological linear spaces; Choquet theory

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 3 , December 1982 , pp. 394 - 400
Copyright
Copyright © Australian Mathematical Society 1982

References

Bibliographie

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