Families of sets of positive measure

Plebanek, Grzegorz

doi:10.1090/S0002-9947-1992-1044965-6

Families of sets of positive measure
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Trans. Amer. Math. Soc. 332 (1992), 181-191 Request permission

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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Remarques sur les fonctions completement additives et sur les ensembles jouissant de la propriete de Baire

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