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A Stone-Weierstrass Theorem Without Closure Under Suprema
| Content Provider | Scilit |
|---|---|
| Author | McAfee, R. Preston Reny, Philip J. |
| Copyright Year | 1992 |
| Description | For a compact metric space $X$, consider a linear subspace $A$ of $C\left ( X \right )$ 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 $C\left ( X \right )$. By the Hahn-Banach Theorem, if $A$ separates probability measures, $A$ is dense in $C\left ( X \right )$. It is shown that if $A$ separates points from probability measures, then the closure of $A$ under minima is dense in $C\left ( X \right )$. This theorem has applications in economic theory. |
| Related Links | https://www.ams.org/proc/1992-114-01/S0002-9939-1992-1091186-2/S0002-9939-1992-1091186-2.pdf |
| Ending Page | 67 |
| Page Count | 7 |
| Starting Page | 61 |
| ISSN | 00029939 |
| e-ISSN | 10886826 |
| DOI | 10.2307/2159783 |
| Journal | Proceedings of the American Mathematical Society |
| Issue Number | 1 |
| Volume Number | 114 |
| Language | English |
| Publisher | Duke University Press |
| Publisher Date | 1992-01-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Physics Weierstrass Theorem Stone Weierstrass Functions Compact Hahn Suprema Subspace |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
