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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A general condition for lifting theorems


Author: E. Arthur Robinson
Journal: Trans. Amer. Math. Soc. 330 (1992), 725-755
MSC: Primary 28D05; Secondary 28D20
DOI: https://doi.org/10.1090/S0002-9947-1992-1040044-2
MathSciNet review: 1040044
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Abstract: We define a general condition, called stability on extensions $ T$ of measure preserving transformations $ S$. Stability is defined in terms of relative unique ergodicity, and as a joining property. Ergodic compact group extensions are stable, and moreover stable extensions satisfy lifting theorems similar to those satisfied by group extensions. In general, stable extensions have relative entropy zero. In the class of continuous flow extensions over strictly ergodic homeomorphisms, stable extensions are generic.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1040044-2
Keywords: Ergodic theory
Article copyright: © Copyright 1992 American Mathematical Society