Kwiatkowsky, Jan; Lemańczyk, Mariusz 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 Keywords:ergodic automorphism; pure point spectrum; centralizer; weakly mixing two-fold simple automorphisms Citations:Zbl 0686.00015 PDFBibTeX XML