Some invariant 𝜎-algebras for measure-preserving transformations

Walters, Peter

doi:10.1090/S0002-9947-1972-0291413-7

Some invariant $\sigma$-algebras for measure-preserving transformations
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Trans. Amer. Math. Soc. 163 (1972), 357-368 Request permission

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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Metric properties of transformations of $G$-spaces