Mixing Sets for Rigid Transformations

It is shown that, for any infinite set of density zero, there exists a rigid measure-preserving transformation of a probability space which is mixing along . As examples, Gaussian actions and Poisson suspensions over infinite rank-one constructions are considered. Analogues of the obtained result fo...

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Bibliographic Details
Published in:Mathematical Notes 2021-09, Vol.110 (3-4), p.565-570
Main Author: Ryzhikov, V. V.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Mathematics
Mathematics and Statistics
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Summary:It is shown that, for any infinite set of density zero, there exists a rigid measure-preserving transformation of a probability space which is mixing along . As examples, Gaussian actions and Poisson suspensions over infinite rank-one constructions are considered. Analogues of the obtained result for group actions and a method not using Gaussian and Poisson suspensions are also discussed.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434621090261