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Transactions of the American Mathematical Society

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

 

 

Some invariant $ \sigma $-algebras for measure-preserving transformations


Author: Peter Walters
Journal: Trans. Amer. Math. Soc. 163 (1972), 357-368
MSC: Primary 28A65
MathSciNet review: 0291413
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Abstract: For an invertible measure-preserving transformation $ T$ of a Lebesgue measure space $ (X,\mathcal{B},m)$ and a sequence $ N$ of integers, a $ T$-invariant partition $ {\alpha _N}(T)$ of $ (X,\mathcal{B},m)$ is defined. The relationship of these partitions to spectral properties of $ T$ and entropy theory is discussed and the behaviour of the partitions $ {\alpha _N}(T)$ under group extensions is investigated. Several examples are discussed.


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DOI: https://doi.org/10.1090/S0002-9947-1972-0291413-7
Keywords: Measure-preserving transformation, ergodic, partition, $ \sigma $-algebra, entropy, mixing, spectral measure, group extension, Gaussian process
Article copyright: © Copyright 1972 American Mathematical Society