Hyperfiniteness and the Halmos-Rohlin Theorem for Nonsingular Abelian Actions
Open Access
- 1 March 1976
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 55 (2) , 339-344
- https://doi.org/10.2307/2041720
Abstract
Theorem 1. Let the countable abelian group act nonsingularly and aperiodically on Lebesgue space . Then for each finite subset <!-- MATH $A \subset G$ --> and <!-- MATH $\varepsilon > 0\exists$ --> 0\exists $"> finite <!-- MATH $B \subset G$ --> and <!-- MATH $F \subset X$ --> with <!-- MATH $\{ bF:b \in B\}$ --> disjoint and <!-- MATH $\mu [({ \cap _{a \in A}}B - a)F] > 1 - \varepsilon$ --> 1 - \varepsilon $">.
Keywords
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