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A Stone-Weierstrass Theorem without closure under suprema

McAfee, R. Preston and Reny, Philip J. (1992) A Stone-Weierstrass Theorem without closure under suprema. Proceedings of the American Mathematical Society, 114 (1). pp. 61-67. ISSN 0002-9939. doi:10.1090/S0002-9939-1992-1091186-2. https://resolver.caltech.edu/CaltechAUTHORS:20171108-162257007

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Abstract

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). By the Hahn-Banach Theorem, if A separates probability measures, A is dense in C(X). It is shown 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.


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https://doi.org/10.1090/S0002-9939-1992-1091186-2 DOIArticle
http://www.ams.org/journals/proc/1992-114-01/S0002-9939-1992-1091186-2/PublisherArticle
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Additional Information:© 1992 American Mathematical Society. Received by the editors April 6, 1990. 1991 Mathematics Subject Classification. Primary 46B28, 26A15. The authors gratefully acknowledge the assistance of Charalambos Aliprantis in the preparation of this paper. Communicated by Palle E. T. Jorgensen. Formerly SSWP 727.
Issue or Number:1
DOI:10.1090/S0002-9939-1992-1091186-2
Record Number:CaltechAUTHORS:20171108-162257007
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20171108-162257007
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ID Code:83095
Collection:CaltechAUTHORS
Deposited By: Jacquelyn Bussone
Deposited On:16 Nov 2017 22:50
Last Modified:15 Nov 2021 19:55

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