ON THE VITALI-HAHN-SAKS-NIKODYM THEOREM
作者:
Paul Abraham,
期刊:
Quaestiones Mathematicae
(Taylor Available online 1996)
卷期:
Volume 19,
issue 3-4
页码: 397-407
ISSN:1607-3606
年代: 1996
DOI:10.1080/16073606.1996.9631985
出版商: Taylor & Francis Group
关键词: 46B20;46G10
数据来源: Taylor
摘要:
The classical Vitali-Hahn-Saks-Nikodym Theorem [5, Thm. I.4.8] gives a limit criterion for when a sequence of strongly additive vector measures on a σ-field of sets having their range in a Banach space can be expected to be uniformly strongly additive. In [16, Cor. 8], Saeki proved that the limit condition on the sequence of vector measures could be substantially weakened as long as the Banach space in play is “good enough”. Saeki's result was based upon his work on a class of set functions too large to have Rosenthal's Lemma at his disposal. In Section 2, we prove Saeki's result with Rosenthal's Lemma at the basis of our work and then augment our characterization of Banach spaces enjoying Saeki's result in [1] with another natural equivalent condition. In Section 3 we extend Saeki's result to Boolean algebras having the Subsequential Interpolation property.
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