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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
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Abstract

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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

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