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Measures on Boolean algebras


Author: Wiesław Główczyński
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
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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 [Enhancements On Off] (What's this?)

  • [Du] R. M. Dudley, On sequential convergence, Trans. Amer. Math. Soc. 112 (1964), 483-507. MR 0175081 (30:5266)
  • [D] E. K. van Douwen, The integers and topology, Handbook of Set-theoretic Topology, North-Holland, 1984, pp. 111-167. MR 776622 (87f:54008)
  • [E] R. Engelking, General topology, PWN, Warsaw, 1977. MR 0500780 (58:18316b)
  • [F] D. Fremlin, Measure algebras, Handbook of Boolean Algebras, North Holland, 1989. MR 991611
  • [G] H. Gaifman, Concerning measures on Boolean algebras, Pacific J. Math. 14 (1964), 61-73. MR 0161952 (28:5156)
  • [J] T. Jech, Set theory, Academic Press, New York, 1978. MR 506523 (80a:03062)
  • [K] J. L. Kelley, Measures on Boolean algebras, Pacific J. Math. 9 (1959), 1165-1177. MR 0108570 (21:7286)
  • [Ki] J. Kisyński, Convergence due type $ L$, Coll. Math. 7 (1960), 205-211. MR 0123287 (23:A615)
  • [Ku] K. Kunen, Set theory, North Holland, Amsterdam, 1980. MR 597342 (82f:03001)
  • [M] D. Maharam, An algebraic characterisation of measure algebras, Ann. Math. 48 (1947), 153-167. MR 0018718 (8:321b)
  • [MS] V. Malyhin and B. E. Shapirowski, Martin axiom and properties of topological spaces, Dokl. Akad. Nauk USSR 213 (1973), 532-533. (Russian)
  • [S] L. A. Savelev, On order topology and continuous measures, Sibirsky Math. J. 6 (1965), 1356-1364. (Russian)
  • [V1] D. A. Vladimirov, On completeness of semiordered spaces, Uspekhy Mat. Nauk 15 (1960), 164-172. (Russian) MR 0114106 (22:4933)
  • [V2] -, Boolean algebras, Nauka, Moscow, 1969. (Russian) MR 0263713 (41:8314)
  • [V3] -, Mathematical encyclopedia, vol. 4, Soviet. Enc., Moscow, 1984, p. 937. (Russian)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1050019-X
Article copyright: © Copyright 1991 American Mathematical Society

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