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Ergodic properties that lift to compact group extensions. (English) Zbl 0636.28007
Summary: Let T and R be measure preserving, T weakly mixing, R ergodic, and let S be conservative ergodic and nonsingular. Let T ˜ be a weakly mixing compact Abelian group extension of T. If T×S is ergodic then T ˜×S is ergodic. A corollary is a new proof that if T is mildly mixing then so is T ˜· A similar statement holds for other ergodic multiplier properties. Now let T ˜ be a weakly mixing type α compact affine G extension of T where α is an automorphism of G. If T and R are disjoint and α or R has entropy zero, then T ˜ and R are disjoint. T ˜ is uniquely ergodic if and only if T is uniquely ergodic and α has entropy zero. If T is mildly mixing and T ˜ is weakly mixing then T ˜ is mildly mixing. We also provide a new proof that if T ˜ is weakly mixing then T ˜ has the K-property if T does.

MSC:
28D05Measure-preserving transformations
28D20Entropy and other measure-theoretic invariants