Infinite measure preserving transformations with Radon MSJ

We introduce concepts of Radon MSJ and Radon disjointness for infinite Radon measure preserving homeomorphisms of the locally compact Cantor space. We construct an uncountable family of pairwise Radon disjoint infinite Chacon like transformations. Every such transformation is Radon strictly ergodic,...

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Bibliographic Details
Published in:Israel journal of mathematics 2018-10, Vol.228 (1), p.21-51
Main Author: Danilenko, Alexandre I.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Ergodic processes
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Radon
Theoretical
Topology
Transformations
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Summary:We introduce concepts of Radon MSJ and Radon disjointness for infinite Radon measure preserving homeomorphisms of the locally compact Cantor space. We construct an uncountable family of pairwise Radon disjoint infinite Chacon like transformations. Every such transformation is Radon strictly ergodic, totally ergodic, asymmetric (not isomorphic to its inverse), has Radon MSJ and possesses Radon joinings whose ergodic components are not joinings.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-018-1746-5