Finite Borel measures on spaces of cardinality less than $\mathfrak {c}$
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- by R. J. Gardner and G. Gruenhage PDF
- Proc. Amer. Math. Soc. 81 (1981), 624-628 Request permission
Abstract:
Let $\kappa < c$ be uncountable. We prove, among other results, that every $\alpha$-realcompact space of cardinality $\kappa$ is Borel measure-compact if and only if there is a set of reals of cardinality $\kappa$ whose Lebesgue measure is not zero.References
-
F. R. Drake, Set theory, North-Holland, London, 1974.
- Nancy Dykes, Generalizations of realcompact spaces, Pacific J. Math. 33 (1970), 571–581. MR 276928
- D. H. Fremlin, Uncountable powers of $\textbf {R}$ can be almost Lindelöf, Manuscripta Math. 22 (1977), no. 1, 77–85. MR 464155, DOI 10.1007/BF01182068
- R. J. Gardner, The regularity of Borel measures and Borel measure-compactness, Proc. London Math. Soc. (3) 30 (1975), 95–113. MR 367145, DOI 10.1112/plms/s3-30.1.95
- Anthony W. Hager, George D. Reynolds, and M. D. Rice, Borel-complete topological spaces, Fund. Math. 75 (1972), no. 2, 135–143. MR 309071, DOI 10.4064/fm-75-2-135-143
- Paul R. Halmos, Measure Theory, D. Van Nostrand Co., Inc., New York, N. Y., 1950. MR 0033869
- Richard Haydon, On compactness in spaces of measures and measurecompact spaces, Proc. London Math. Soc. (3) 29 (1974), 1–16. MR 361745, DOI 10.1112/plms/s3-29.1.1 K. Kunen, Inaccessibility properties of cardinals, Doctoral Dissertation, Stanford Univ., 1968.
- Dorothy Maharam, On homogeneous measure algebras, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 108–111. MR 6595, DOI 10.1073/pnas.28.3.108
- D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), no. 2, 143–178. MR 270904, DOI 10.1016/0003-4843(70)90009-4
- Washek F. Pfeffer, Integrals and measures, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 42, Marcel Dekker, Inc., New York-Basel, 1977. MR 0460580
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 624-628
- MSC: Primary 54H99; Secondary 03E15, 04A15, 28A12, 54D20, 54G20
- DOI: https://doi.org/10.1090/S0002-9939-1981-0601743-5
- MathSciNet review: 601743