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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Weakly dense subsets of the measure algebra


Author: Maxim R. Burke
Journal: Proc. Amer. Math. Soc. 106 (1989), 867-874
MSC: Primary 28A51; Secondary 06E99, 54A25
DOI: https://doi.org/10.1090/S0002-9939-1989-0961402-3
MathSciNet review: 961402
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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


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DOI: https://doi.org/10.1090/S0002-9939-1989-0961402-3
Article copyright: © Copyright 1989 American Mathematical Society