Weakly dense subsets of the measure algebra

Burke, Maxim R.

doi:10.1090/S0002-9939-1989-0961402-3

Weakly dense subsets of the measure algebra
HTML articles powered by AMS MathViewer

by Maxim R. Burke PDF

Proc. Amer. Math. Soc. 106 (1989), 867-874 Request permission

Abstract:

We introduce the notion of the weak density of a Boolean algebra and show that for homogeneous measure algebras it coincides with the density (=least size of a coinitial set). From this we obtain a partial lifting of the measure algebra of $\left [ {0,1} \right ]$ of minimal size which does not extend to a lifting. It also follows that the $\pi$-character of each point and the $\pi$-weight are the same for the Stone space of a homogeneous measure algebra

References

A theorem on lifting

J. Cichoń, A. Kamburelis, and J. Pawlikowski, On dense subsets of the measure algebra, Proc. Amer. Math. Soc. 94 (1985), no. 1, 142–146. MR 781072, DOI 10.1090/S0002-9939-1985-0781072-3
Eric K. van Douwen, Cardinal functions on Boolean spaces, Handbook of Boolean algebras, Vol. 2, North-Holland, Amsterdam, 1989, pp. 417–467. MR 991599

On two theorems of Mokobodzki

D. H. Fremlin, On the additivity and cofinality of Radon measures, Mathematika 31 (1984), no. 2, 323–335 (1985). MR 804206, DOI 10.1112/S0025579300012535
Casper Goffman, Real functions, Rinehart & Co., Inc., New York, N. Y., 1953. MR 0054006
Paul R. Halmos, Measure Theory, D. Van Nostrand Co., Inc., New York, N. Y., 1950. MR 0033869
R. Hodel, Cardinal functions. I, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 1–61. MR 776620
Thomas Jech, Set theory, Pure and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 506523
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
Menachem Magidor, On the singular cardinals problem. I, Israel J. Math. 28 (1977), no. 1-2, 1–31. MR 491183, DOI 10.1007/BF02759779
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
John C. Oxtoby, Measure and category, 2nd ed., Graduate Texts in Mathematics, vol. 2, Springer-Verlag, New York-Berlin, 1980. A survey of the analogies between topological and measure spaces. MR 584443
Walter Rudin, Well-distributed measurable sets, Amer. Math. Monthly 90 (1983), no. 1, 41–42. MR 691011, DOI 10.2307/2975692
Roman Sikorski, Boolean algebras, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 25, Academic Press, Inc., New York; Springer-Verlag, Berlin-New York, 1964. MR 0177920