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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