Ergodic properties that lift to compact group extensions

Author:
E. Arthur Robinson

Journal:
Proc. Amer. Math. Soc. **102** (1988), 61-67

MSC:
Primary 28D05

DOI:
https://doi.org/10.1090/S0002-9939-1988-0915717-4

MathSciNet review:
915717

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Abstract: Let and be measure preserving, weakly mixing, ergodic, and let be conservative ergodic and nonsingular. Let be a weakly mixing compact abelian group extension of . If is ergodic then is ergodic. A corollary is a new proof that if is mildly mixing then so is . A similar statement holds for other ergodic multiplier properties. Now let be a weakly mixing type compact affine extension of where is an automorphism of . If and are disjoint and or has entropy zero, then and are disjoint. is uniquely ergodic if and only if is uniquely ergodic and has entropy zero. If is mildly mixing and is weakly mixing then is mildly mixing. We also provide a new proof that if is weakly mixing then has the -property if does.

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DOI:
https://doi.org/10.1090/S0002-9939-1988-0915717-4

Article copyright:
© Copyright 1988
American Mathematical Society