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A \(\sigma\)-linked Boolean algebra without positive measure. (English) Zbl 0688.06010
An example is given of a Boolean algebra which has no positive measure but which is \(\sigma\)-linked.
Reviewer: R.Potock√Ĺ

MSC:
06E10 Chain conditions, complete algebras
60A10 Probabilistic measure theory
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[1] Bell, M.G., Two Boolean algebras with extreme cellular and compactness properties, Canad. J. math., 35, 824-838, (1983) · Zbl 0519.06012
[2] van Douwen, E.K., Nonsupercompactness and the reduced measure algebra, Comment. math. univ. carolin., 21, 507-512, (1980) · Zbl 0437.54014
[3] Gaifman, H., Concerning measures on Boolean algebras, Pacific J. math., 14, 61-73, (1963) · Zbl 0127.02306
[4] Hodges, J.L.; Horn, A., On Maharam’s conditions for a measure, Trans. amer. math. soc., 64, 594-595, (1948) · Zbl 0032.14901
[5] Horn, A.; Tarski, A., Measures in Boolean algebras, Trans. amer. math. soc., 64, 467-497, (1948) · Zbl 0035.03001
[6] Kelley, J.L., Measures in Boolean algebras, Pacific J. math., 9, 1165-1177, (1959) · Zbl 0087.04801
[7] Maharam, D., An algebraic characterization of measure algebras, Ann. of math., 48, 154-167, (1947) · Zbl 0029.20401
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