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The centralizer of ergodic theory group extensions. (English) Zbl 0695.28006

Dynamical systems and ergodic theory, 28th Sem. St. Banach Int. Math. Cent., Warsaw/Pol. 1986, Banach Cent. Publ. 23, 455-463 (1989).
[For the entire collection see Zbl 0686.00015.]
It is proved that for an ergodic automorphism T with pure point spectrum and its ergodic G-extension \(T_{\phi}\) (G is a compact metric Abelian group) the set \(X_ 0\subset X\) of those x’s which lift to the centralizer of \(T_{\phi}\) is of Haar measure zero. Some related problems for weakly mixing two-fold simple automorphisms are considered.
Reviewer: J.Šiška

MSC:

28D05 Measure-preserving transformations

Citations:

Zbl 0686.00015