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 of minimal size which does not extend to a lifting. It also follows that the -character of each point and the -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