Density of infimum-stable convex cones
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- by João B. Prolla PDF
- Proc. Amer. Math. Soc. 121 (1994), 175-178 Request permission
Abstract:
Let X be a compact Hausdorff space and let A be a linear subspace of $C(X;\mathbb {R})$ containing the constant functions, and separating points from probability measures. Then the inf-lattice generated by A is uniformly dense in $C(X;\mathbb {R})$. We show that this is a corollary of the Choquet-Deny Theorem, thus simplifying the proof and extending to the nonmetric case a result of McAfee and Reny.References
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- R. Preston McAfee and Philip J. Reny, A Stone-Weierstrass theorem without closure under suprema, Proc. Amer. Math. Soc. 114 (1992), no. 1, 61–67. MR 1091186, DOI 10.1090/S0002-9939-1992-1091186-2
- Leopoldo Nachbin, Elements of approximation theory, Van Nostrand Mathematical Studies, No. 14, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0217483
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 175-178
- MSC: Primary 46E05; Secondary 41A65, 46A55
- DOI: https://doi.org/10.1090/S0002-9939-1994-1186134-2
- MathSciNet review: 1186134