Abstract
AbstractLet 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.
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Schedule a callMore From: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
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