次等价关系与正定函数
Subequivalence Relations and Positive-Definite Functions
摘要：
研究了标准概率空间上保测度等价关系的正定函数，并用它来定量地度量次等价关系的接近性.这是结合最近的共同诱导建设爱泼斯坦产生新的混合行动的任意无限离散群，它也被用来表明，轨道等价的自由，措施保持，混合行动的非顺从的群体是不可分类的在很强的意义。最后，在性质（T）群的情况下，我们讨论了Cayley图上具有不变渗流的连接和成本的计算。
英文摘要：
We study a positive-definite function associated to a measure-preserving equivalence relation on a standard probability space and use it to measure quantitatively the proximity of subequivalence relations. This is combined with a recent co-inducing construction of Epstein to produce new kinds of mixing actions of an arbitrary infinite discrete group and it is also used to show that orbit equivalence of free, measure preserving, mixing actions of non-amenable groups is unclassifiable in a strong sense. Finally, in the case of property (T) groups we discuss connections with invariant percolation on Cayley graphs and the calculation of costs.
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