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The Stone--Weierstrass Theorem and Spaces of Measures

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Abstract

Results concerning the Stone--Weierstrass theorems for completely regular spaces are obtained.

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REFERENCES

  1. E. Hewitt, “Certain generalizations of the Weierstrass approximation theorem,” Duke Math. J., 14 (1947), 419-427.

    Google Scholar 

  2. R. Giles, “A generalization of the strict topology,” Trans. Amer. Math. Soc., 161 (1971), 467-474.

    Google Scholar 

  3. R. Engelking, General Topology, PWN, Warsaw, 1983.

    Google Scholar 

  4. N. Bourbaki, Éléments de mathématique. Livre III. Topologie générale, ch. IX et X, Hermann, Paris, 1948, 1949.

    Google Scholar 

  5. H. Schaefer, Topological Vector Spaces, Macmillan, New York, 1966.

    Google Scholar 

  6. A. D. Aleksandrov, “Additive set functions in abstract spaces, I,” Mat. Sb. [Math. USSR-Sb.], 8 (1940), 307-348; “II,” Mat. Sb. [Math. USSR-Sb.], 9 (1941), 563-628; “III,” Mat. Sb. [Math. USSR-Sb.], 13 (1943), 169-238.

    Google Scholar 

  7. V. S. Varadarain, “Measures on topological spaces,” Mat. Sb. [Math. USSR-Sb.], 55 (97) (1961), 35-100.

    Google Scholar 

  8. J. D. Knowles, “Measures on topological spaces,” Proc. London Math. Soc. (3), 17 (1967), 139-156.

  9. V. P. Fedorova, “A dual characterization of the completion and completeness of a uniform space,” Mat. Sb. [Math. USSR-Sb.], 64 (106) (1964), 632-639.

    Google Scholar 

  10. G. I. O. Jameson, “Topological M-spaces,” Math. Z., 103 (1968), 139-150.

    Google Scholar 

  11. V. P. Fedorova, “Integral representations of functionals on spaces of uniformly continuous functions,” Sibirsk. Mat. Zh. [Siberian Math. J.], 23 (1982), no. 5, 205-218.

    Google Scholar 

  12. G. G. Gould and M. Mahowald, “Measures on completely regular spaces,” J. London Math. Soc., 37 (1962), 103-111.

    Google Scholar 

  13. D. A. Raikov, “Free locally convex spaces of uniform spaces,” Mat. Sb. [Math. USSR-Sb.], 63 (105) (1964), 582-590.

    Google Scholar 

  14. V. P. Fedorova, “Linear functionals on spaces of uniformly continuous functions and abstract measures,” Mat. Zametki [Math. Notes], 36 (1984), no. 5, 743-754.

    Google Scholar 

  15. E. Hewitt, “Linear functionals on spaces of continuous functions,” Fund. Math., 37 (1950), 161-189.

    Google Scholar 

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Fedorova, V.P. The Stone--Weierstrass Theorem and Spaces of Measures. Mathematical Notes 72, 417–427 (2002). https://doi.org/10.1023/A:1020511807357

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  • DOI: https://doi.org/10.1023/A:1020511807357

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