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$${\mathbb{Z}}^ n$$ and $${\mathbb{R}}^ n$$ cocycle extensions and complementary algebras. (English) Zbl 0625.28008
Let T be an ergodic measure-preserving map on a Lebesgue space X, $$S=\{S_ g\}_{g\in G}^ a$$measure-preserving free action of $$G={\mathbb{Z}}^ n$$ or $${\mathbb{R}}^ n$$ on a Lebesgue space Y, and let $$f: X\times {\mathbb{Z}}\to G$$ be a cocycle. Let $$\hat T$$ be the extension of T (by S and f) defined by $$\hat T^ n(x,y)=(T^ nx,S_{f(x,n)}y)$$ for $$(x,y)\in X\times Y$$. The author studies how weak mixing and the K-system property lift from T to $$\hat T$$ if $$\hat T$$ is ergodic. The technical proofs make use of measure algebras and Rochlin towers.
Reviewer: F.M.Dekking

##### MSC:
 28D05 Measure-preserving transformations
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##### References:
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