Decompositions and measures on countable Borel equivalence relations
Decompositions and measures on countable Borel equivalence relations
复制标题
可数Borel等价关系的分解与测度
DOI：
10.1017/etds.2020.119
复制
发表时间：
2018
影响因子：
0.9
通讯作者：
Ruiyuan Chen
中科院分区：
文献类型：
--
作者：
Ruiyuan Chen
本文证明了可数Borel等价关系的一致测度论遍历分解
（X，E）
可以实现为可数群的连续作用的拓扑遍历分解
$\Gamma \curvearrowright X$
产生E.然后，我们将其应用于基数代数的研究
$\mathcal {K}（E）$
关于可压缩可数Borel等价关系的Borel集的等分解型
（X，E）
.我们还提出了一些一般的意见，商拓扑遍历分解，与应用弱等价的措施保持行动。
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 observations regarding quotient topologies on topological ergodic decompositions, with an application to weak equivalence of measure-preserving actions.