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Universal Lusin measurability and subfamily summable families in abelian topological groups

Author: William H. Graves
Journal: Proc. Amer. Math. Soc. 73 (1979), 45-50
MSC: Primary 28C10; Secondary 46G99
MathSciNet review: 512056
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Abstract: It is proved that if G is a Hausdorff abelian topological group with respect to topologies $ \alpha \subseteq \beta $ such that $ \beta $ is complete and the identity map of $ (G,\alpha )$ onto $ (G,\beta )$ is universally Lusin measurable, then the subfamily summable families are the same for $ \alpha $ and $ \beta $.

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Keywords: Orlicz-Pettis theorem, subfamily summable families, abelian group-valued measures, universal measurability
Article copyright: © Copyright 1979 American Mathematical Society