Ergodic Subequivalence Relations Induced by a Bernoulli Action
Ergodic Subequivalence Relations Induced by a Bernoulli Action
复制标题
DOI：
10.1007/s00039-010-0058-7
复制
发表时间：
2008-02
影响因子：
2.2
通讯作者：
I. Chifan;A. Ioana
中科院分区：
文献类型：
--
作者：
I. Chifan;A. Ioana
设Γ为可数群，用伯努利作用诱导的等价关系表示，其中[0,1]Γis赋与积勒贝格测度。证明了对于任意的子等价关系，对于[0,1]Γinto-invariant可测集存在一个分区{Xi}i≥0，使得对于每一个i≥1都是超有限和强遍历的（因此是遍历的和非超有限的）。
Let Γ be a countable group and denote bythe equivalence relation induced by the Bernoulli action, where [0, 1]Γis endowed with the product Lebesgue measure. We prove that, for any subequivalence relationof, there exists a partition {Xi}i≥0of [0, 1]Γinto-invariant measurable sets such thatis hyperfinite andis strongly ergodic (hence ergodic and non-hyperfinite), for everyi≥ 1.