Published January 1992
| public
Journal Article
A Stone-Weierstrass Theorem without closure under suprema
- Creators
- McAfee, R. Preston
- Reny, Philip J.
Chicago
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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.
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.Additional details
- Eprint ID
- 83095
- Resolver ID
- CaltechAUTHORS:20171108-162257007
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