论文标题
自由团体无与伦比的行动
Incomparable actions of free groups
论文作者
论文摘要
假设$ x $是波兰的空间，$ e $是$ x $上的可数鲍尔等效关系，而$μ$是$ x $的$ e $ $ e $ invariant borel概率度量。我们考虑在每个可数的非亚伯利亚自由组$γ$的情况下，都有一个borel序列$（\ cdot_r）_ {r \ in \ mathbb {r}} $ $ x $上的$γ$的免费操作，从$（e_r）_ {r \ in \ mathbb {r}} $是越来越多的关系顺序，在$μ$可重新确定下是成对无与伦比的。特别是，我们表明，如果$ e $满足自然可分离性条件，那么只要存在于$ x $上的可数字非亚洲自由群体的免费Borel动作，从而产生了$ E $的非等价关系，而$μ$是$μ$。
Suppose that $X$ is a Polish space, $E$ is a countable Borel equivalence relation on $X$, and $μ$ is an $E$-invariant Borel probability measure on $X$. We consider the circumstances under which for every countable non-abelian free group $Γ$, there is a Borel sequence $(\cdot_r)_{r \in \mathbb{R}}$ of free actions of $Γ$ on $X$, generating subequivalence relations $E_r$ of $E$ with respect to which $μ$ is ergodic, with the further property that $(E_r)_{r \in \mathbb{R}}$ is an increasing sequence of relations which are pairwise incomparable under $μ$-reducibility. In particular, we show that if $E$ satisfies a natural separability condition, then this is the case as long as there exists a free Borel action of a countable non-abelian free group on $X$, generating a subequivalence relation of $E$ with respect to which $μ$ is ergodic.
