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A Stone-Weierstrass Theorem without Closure under Suprema

McAfee, R. Preston and Reny, Philip J. (1990) A Stone-Weierstrass Theorem without Closure under Suprema. Social Science Working Paper, 727. California Institute of Technology , Pasadena, CA. (Unpublished)

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For a compact metric space X, consider a linear subspace A of C (X) containing the constant functions. One version of the Stone-Weierstrass theorem states that, if A separates points, then the closure of A under both minima and maxima is dense in C (X). Similarly, by the Hahn-Banach theorem, if A separates probability measures, A is dense in C (X). We show that if A separates points from probability measures, then the closure of A under minima is dense in C (X). This theorem has applications in Economic Theory.

Item Type:Report or Paper (Working Paper)
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Additional Information:The authors gratefully acknowledge the assistance of Charalambos Aliprantis in the preparation of this paper. Published as McAfee, R. Preston, and Philip J. Reny. "A Stone-Weierstrass theorem without closure under suprema." Proceedings of the American Mathematical Society 114, no. 1 (1992): 61-67.
Group:Social Science Working Papers
Series Name:Social Science Working Paper
Issue or Number:727
Classification Code:MSC: 41A65; 41A10, 46E25, 54C40
Record Number:CaltechAUTHORS:20170901-135500931
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81084
Deposited By: Jacquelyn Bussone
Deposited On:05 Sep 2017 23:53
Last Modified:03 Oct 2019 18:38

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