论文标题
$ out（f_n）$ - 在$ n $生成的群体的空间上不变的概率度量
$Out(F_n)$-invariant probability measures on the space of $n$-generated marked groups
论文作者
论文摘要
令$ \ Mathcal g_n $表示$ n $生成的标记组的空间。我们证明，对于每一个$ n \ ge 2 $，都存在$ 2^{\ aleph_0} $ non-ratomic，$ out（f_n）$ - 不变，在$ \ mathcal g_n $上进行混合概率措施。另一方面，有$ \ mathcal g_n $的非空封闭子集承认没有$ out（f_n）$ - 不变概率度量。组$ aut（f_n）$的酰基轴承双曲线在两种结果的证明中都起着至关重要的作用。我们还讨论了$ out（f_n）$的存在的模型理论含义 - $ \ mathcal g_n $不变的，ergodic的概率度量。
Let $\mathcal G_n$ denote the space of $n$-generated marked groups. We prove that, for every $n\ge 2$, there exist $2^{\aleph_0}$ non-atomic, $Out(F_n)$-invariant, mixing probability measures on $\mathcal G_n$. On the other hand, there are non-empty closed subsets of $\mathcal G_n$ that admit no $Out(F_n)$-invariant probability measure. Acylindrical hyperbolicity of the group $Aut(F_n)$ plays a crucial role in the proof of both results. We also discuss model theoretic implications of the existence of $Out(F_n)$-invariant, ergodic probability measures on $\mathcal G_n$.
