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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Families of sets of positive measure


Author: Grzegorz Plebanek
Journal: Trans. Amer. Math. Soc. 332 (1992), 181-191
MSC: Primary 28A12; Secondary 28C15
DOI: https://doi.org/10.1090/S0002-9947-1992-1044965-6
MathSciNet review: 1044965
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Abstract: We present a combinatorial description of those families $ \mathcal{P}$ of sets, for which there is a finite measure $ \mu $ such that $ \inf \{ \mu (P):P \in \mathcal{P}\} > 0$. This result yields a topological characterization of measure-compactness and Borel measure-compactness. It is also applied to a problem on the existence of regular measure extensions.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1044965-6
Article copyright: © Copyright 1992 American Mathematical Society