论文标题
等距轨道等效性，用于保存概率的操作
Isometric orbit equivalence for probability-measure preserving actions
论文作者
论文摘要
我们研究了通过定义的图形来保存（P.M.P.）的概率测量（P.M.P.）。我们介绍并研究了P.M.P.等轴测轨道等效的概念。行动：两个下午如果由组的某些固定生成系统定义的绘制图是等距的，则作用是等效轨道等效的。我们强调了两种现象。首先，我们证明，对于固定生成系统，等距轨道等效性的概念对于cayley图具有可计数的自动形态的组是刚性的。另一方面，我们引入了等值轨道等效P.M.P.的一般结构。动作，导致等距轨道等效P.M.P.的有趣的非平凡示例。自由小组的行动。特别是，我们的示例表明，在等距轨道等效性下，混合并不是不变的。
We study probability-measure preserving (p.m.p.) actions of finitely generated groups via the graphings they define. We introduce and study the notion of isometric orbit equivalence for p.m.p. actions: two p.m.p. actions are isometric orbit equivalent if the graphings defined by some fixed generating systems of the groups are measurably isometric. We highlight two kind of phenomena. First, we prove that the notion of isometric orbit equivalence is rigid for groups whose Cayley graph, with respect to a fixed generating system, has a countable group of automorphism. On the other hand, we introduce a general construction of isometric orbit equivalent p.m.p. actions, which leads to interesting nontrivial examples of isometric orbit equivalent p.m.p. actions for the free group. In particular, our examples show that mixing is not invariant under isometric orbit equivalence.
