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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

The Vitali-Hahn-Saks theorem for Boolean algebras with the subsequential interpolation property


Author: Francisco José Freniche
Journal: Proc. Amer. Math. Soc. 92 (1984), 362-366
MSC: Primary 28A33; Secondary 06E10, 28A60
MathSciNet review: 759653
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Abstract: It is shown that the Vitali-Hahn-Saks theorem holds for a new class of Boolean algebras which are defined by a separation property of its disjoint sequences: the Subsequential Interpolation Property. It is also proved that this property is strictly weaker than the Interpolation Property, the $ \left( f \right)$-Property and the Subsequential Completeness Property.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0759653-1
PII: S 0002-9939(1984)0759653-1
Keywords: Boolean algebra, uniformly strongly additive sequence of measures
Article copyright: © Copyright 1984 American Mathematical Society