Decompositions and measures on countable Borel equivalence relations

@article{Chen2020DecompositionsAM,
  title={Decompositions and measures on countable Borel equivalence relations},
  author={Ruiyuan Chen},
  journal={Ergodic Theory and Dynamical Systems},
  year={2020},
  volume={41},
  pages={3671 - 3703}
}
  • Ruiyuan Chen
  • Published 9 January 2018
  • Mathematics
  • Ergodic Theory and Dynamical Systems
Abstract We show that the uniform measure-theoretic ergodic decomposition of a countable Borel equivalence relation $(X, E)$ may be realized as the topological ergodic decomposition of a continuous action of a countable group $\Gamma \curvearrowright X$ generating E. We then apply this to the study of the cardinal algebra $\mathcal {K}(E)$ of equidecomposition types of Borel sets with respect to a compressible countable Borel equivalence relation $(X, E)$ . We also make some general… 
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