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Transactions of the American Mathematical Society

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



Metric properties of transformations of $ G$-spaces

Author: R. K. Thomas
Journal: Trans. Amer. Math. Soc. 160 (1971), 103-117
MSC: Primary 28A65
MathSciNet review: 0293063
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Abstract: The measure-preserving transformation $ T$ acts on a Lebesgue space $ (M,\mathcal{B},\mu )$ which is also a $ G$-space for a compact separable group $ G$. It is proved that if the factor-transformation on the space of $ G$-orbits has completely positive entropy and a certain condition regarding the relations between the actions of $ G$ and $ T$ is satisfied, then $ T$ weakly mixing implies $ T$ has completely positive entropy.

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Keywords: Completely positive entropy, $ G$-space, $ \sigma $-commuting
Article copyright: © Copyright 1971 American Mathematical Society