Non-compact versions of Edwards’ Theorem
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Edwards’ Theorem establishes duality between a convex cone in the space of continuous functions on a compact space X and the set of representing or Jensen measures for this cone. It is a direct consequence of the description of positive superlinear functionals on C(X). In this paper we obtain the description of such functionals when X is a locally compact σ-compact Hausdorff space. As a consequence we prove non-compact versions of Edwards’ Theorem.
KeywordsSuperlinear functionals Envelopes Representing measures Jensen measures
Mathematics Subject Classification46A20 47B65 46A55
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- 2.Aliprantis C.D., Tourky R.: Cones and Duality. Graduate Studies in Mathematics, 84. American Mathematical Society, Providence (2007)Google Scholar
- 3.Edwards, D.A.: Choquet boundary theory for certain spaces of lower semicontinuous functions, in function algebras. In: Proceedings of the international symposium on function algebras, Chicago, pp. 300–309Google Scholar