Descriptive Kakutani equivalence
نویسندگان
چکیده
We consider a descriptive version of Kakutani equivalence for Borel automorphisms of Polish spaces. Answering a question of Nadkarni, we show that up to this notion, there are exactly two Borel automorphisms: those which are smooth, and those which are not. Using this, we classify all Borel R-flows up to C∞ time-change isomorphism. We then extend the notion of Kakutani equivalence to all (not necessarily injective) Borel functions, and provide a variety of results leading towards a full classification of Borel functions on Polish spaces. The main technical tools are a series of Glimm-Effros and Dougherty-Jackson-Kechris style embedding theorems.
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