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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Hyperfiniteness and the Halmos-Rohlin theorem for nonsingular Abelian actions


Authors: J. Feldman and D. A. Lind
Journal: Proc. Amer. Math. Soc. 55 (1976), 339-344
MSC: Primary 28A65; Secondary 46L10
DOI: https://doi.org/10.1090/S0002-9939-1976-0409764-0
MathSciNet review: 0409764
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Abstract: Theorem 1. Let the countable abelian group $ G$ act nonsingularly and aperiodically on Lebesgue space $ (X,\mu )$. Then for each finite subset $ A \subset G$ and $ \varepsilon > 0\exists $ finite $ B \subset G$ and $ F \subset X$ with $ \{ bF:b \in B\} $ disjoint and $ \mu [({ \cap _{a \in A}}B - a)F] > 1 - \varepsilon $.

Theorem 2. Every nonsingular action of a countable abelian group on a Lebesgue space is hyperfinite.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0409764-0
Keywords: Group action, hyperfinite
Article copyright: © Copyright 1976 American Mathematical Society