Measures on Boolean algebras
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- by Wiesław Główczyński
- Proc. Amer. Math. Soc. 111 (1991), 845-849
- DOI: https://doi.org/10.1090/S0002-9939-1991-1050019-X
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Abstract:
We give, under some set-theoretical assumptions, an example of complete, ccc, weakly $(\omega ,\infty )$-distributive, countably generated Boolean algebra without any strictly positive Maharam submeasure.References
- R. M. Dudley, On sequential convergence, Trans. Amer. Math. Soc. 112 (1964), 483–507. MR 175081, DOI 10.1090/S0002-9947-1964-0175081-6
- Eric K. van Douwen, The integers and topology, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 111–167. MR 776622
- Ryszard Engelking, Topologia ogólna, Biblioteka Matematyczna [Mathematics Library], vol. 47, Państwowe Wydawnictwo Naukowe (PWN), Warsaw, 1975 (Polish). MR 0500779
- David H. Fremlin, Measure algebras, Handbook of Boolean algebras, Vol. 3, North-Holland, Amsterdam, 1989, pp. 877–980. MR 991611
- Haim Gaifman, Concerning measures on Boolean algebras, Pacific J. Math. 14 (1964), 61–73. MR 161952
- Thomas Jech, Set theory, Pure and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 506523
- J. L. Kelley, Measures on Boolean algebras, Pacific J. Math. 9 (1959), 1165–1177. MR 108570
- J. Kisyński, Convergence du type ${\cal L}$, Colloq. Math. 7 (1959/60), 205–211 (French). MR 123287, DOI 10.4064/cm-7-2-205-211
- Kenneth Kunen, Set theory, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland Publishing Co., Amsterdam-New York, 1980. An introduction to independence proofs. MR 597342
- Dorothy Maharam, An algebraic characterization of measure algebras, Ann. of Math. (2) 48 (1947), 154–167. MR 18718, DOI 10.2307/1969222 V. Malyhin and B. E. Shapirowski, Martin axiom and properties of topological spaces, Dokl. Akad. Nauk USSR 213 (1973), 532-533. (Russian) L. A. Savelev, On order topology and continuous measures, Sibirsky Math. J. 6 (1965), 1356-1364. (Russian)
- D. A. Vladimirov, On the completeness of a partially ordered space, Uspehi Mat. Nauk 15 (1960), no. 2 (92), 165–172 (Russian). MR 0114106
- D. A. Vladimirov, Bulevy algebry, Izdat. “Nauka”, Moscow, 1969 (Russian). MR 0263713 —, Mathematical encyclopedia, vol. 4, Soviet. Enc., Moscow, 1984, p. 937. (Russian)
Bibliographic Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 845-849
- MSC: Primary 03E50; Secondary 03E35, 06E10, 28A60
- DOI: https://doi.org/10.1090/S0002-9939-1991-1050019-X
- MathSciNet review: 1050019