The structure of hy-per nite Borel equivalence relations

@inproceedings{Dougherty1994TheSO,
  title={The structure of hy-per nite Borel equivalence relations},
  author={Randall L. Dougherty and Steve Jackson and Alexander S. Kechris},
  year={1994}
}
We study the structure of the equivalence relations induced by the orbits of a single Borel automorphism on a standard Borel space. We show that any two such equivalence relations which are not smooth, i.e., do not admit Borel selectors, are Borel embeddable into each other. (This utilizes among other things work of Effros and Weiss.) Using this and also results of Dye, Varadarajan, and recent work of Nadkarni, we show that the cardinality of the set of ergodic invariant measures is a complete… 

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