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 (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20170901-135500931
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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). 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 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170901-135500931 | ||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
ID Code: | 81084 | ||||||
Collection: | CaltechAUTHORS | ||||||
Deposited By: | Jacquelyn Bussone | ||||||
Deposited On: | 05 Sep 2017 23:53 | ||||||
Last Modified: | 03 Oct 2019 18:38 |
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