Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-28T10:28:15.396Z Has data issue: false hasContentIssue false
  • English
  • Français

Mesures coniques et intégrale de Daniell

Part of: Classical measure theory

Published online by Cambridge University Press:  09 April 2009

Richard Becker
Richard Becker
Affiliation:
Equipe d'Analyse, Tour 46, Université Pierre et Marie Curie, 4 place Jussieu, 75230 Paris Cedex 05, 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 a weak space E and h(E) the Riesz space generated by the continuous linear forms on E. A positive conical measure μ on X is a positive linear form on h(E)|x. G. Choquet has proved μ is a Daniell integral on E when E is weakly complete, but μ is not generally a Daniell integral on X. However we give an integration theory for functions on X and compare this theory with the classical Daniell theory. The case where μ is maximal in the sense of G. Choquet is remarkable.

MSC classification

Secondary: 28A25: Integration with respect to measures and other set functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 1 , June 1981 , pp. 46 - 58
Copyright
Copyright © Australian Mathematical Society 1981

References

Bibliographie

[1] Becker, R., ‘Mesures coniques et intégrale de Daniell’, C. R. Acad. Sci. Paris, t. 283, 1976, p. 611–614.Google Scholar
[2] Bourbaki, N., Topologie générale, Chap. 1 et 4, Nouvelle édition (Hermann, Paris, 1971).Google Scholar
[3] Bourbaki, N., Espaces vectoriels topologiques, Chap. 1 et 2, 2e édition (Hermann, Paris, 1963) (Acta. scient. et ind., 1189 a; Bourbaki, 15).Google Scholar
[4] Choquet, G., Lectures on analysis, vol. 1–3. (New York, Amsterdam, W. A. Benjamin, 1969 Mathematics Lecture Note Series).Google Scholar
[5] Riesz, F. et Nagy, B. Sz., Lecons d'analyse fonctionelle, 5e édition. (Paris, Gauthier-Villars, 1968).Google Scholar