zbMATH — the first resource for mathematics

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

06E10 Chain conditions, complete algebras
60A10 Probabilistic measure theory
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.