A Caltech Library Service

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.

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item:


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.

Item Type:Article
Related URLs:
URLURL TypeDescription DOIArticle ItemWorking Paper
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
Record Number:CaltechAUTHORS:20171108-162257007
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83095
Deposited By: Jacquelyn Bussone
Deposited On:16 Nov 2017 22:50
Last Modified:15 Nov 2021 19:55

Repository Staff Only: item control page