Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-23T17:59:51.911Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
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

[1]Becker, R., ‘Some consequences of a kind of Hahn-Banach Theorem,’ Séminaire Choquet, 1977–1978, n° 2.Google Scholar
[2]Choquet, G., Lectures on analysis, Vol. 1–3 (Mathematics Lecture Note Series, Benjamin, New York, Amsterdam, 1969)Google Scholar
[3]Dinges, H., ‘Decomposition in ordered semi-groups,’ J. Functional Analysis 5 (1970), p. 436–83CrossRefGoogle Scholar
[4]de Rugy, A. Goullet, ‘La théorie des cônes biréticulés,’ Ann. Inst. Fourier (Grenoble) 21 (1971).Google Scholar
[5]Thomas, E., ‘Integrals representations in conucluar spaces’, Vector space measures and applications II. Proceedings, Dublin 1977, edited by Aaron, R. M. and Dineen, S., pp. 172–179 (Lecture Notes in Mathematics 645, Springer-Verlag, Berlin, Heidelberg, New York).Google Scholar