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- W4378470714 abstract "Nadkarni's Theorem asserts that for a countable Borel equivalence relation (CBER) exactly one of the following holds: (1) It has an invariant Borel probability measure or (2) it admits a Borel compression, i.e., a Borel injection that maps each equivalence class to a proper subset of it. We prove in this paper an effective version of Nadkarni's Theorem, which shows that if a CBER is effectively Borel, then either alternative (1) above holds or else it admits an effectively Borel compression. As a consequence if a CBER is effectively Borel and admits a Borel compression, then it actually admits an effectively Borel compression. We also prove an effective version of the ergodic decomposition theorem. Finally a counterexample is given to show that alternative (1) above does not admit an effective version." @default.
- W4378470714 created "2023-05-27" @default.
- W4378470714 creator A5061465636 @default.
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- W4378470714 date "2023-05-23" @default.
- W4378470714 modified "2023-09-27" @default.
- W4378470714 title "An effective version of Nadkarni's Theorem" @default.
- W4378470714 doi "https://doi.org/10.48550/arxiv.2305.14518" @default.
- W4378470714 hasPublicationYear "2023" @default.
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