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商品描述
This volume provides a self-contained introduction to some topics in orbit equivalence theory, a branch of ergodic theory. The first two chapters focus on hyperfiniteness and amenability. Included here are proofs of Dye's theorem that probability measure-preserving, ergodic actions of the integers are orbit equivalent and of the theorem of Connes-Feldman-Weiss identifying amenability and hyperfiniteness for non-singular equivalence relations. The presentation here is often influenced by descriptive set theory, and Borel and generic analogs of various results are discussed. The final chapter is a detailed account of Gaboriau's recent results on the theory of costs for equivalence relations and groups and its applications to proving rigidity theorems for actions of free groups.
商品描述(中文翻譯)
本卷提供了對於軌道等價理論（orbit equivalence theory）某些主題的自成一體的介紹，這是隨機理論（ergodic theory）的一個分支。前兩章專注於超有限性（hyperfiniteness）和可容性（amenability）。這裡包括了 Dye 定理的證明，該定理指出保留機率測度的整數隨機作用是軌道等價的，以及 Connes-Feldman-Weiss 定理，該定理識別了非奇異等價關係的可容性和超有限性。這裡的呈現常受到描述集合理論（descriptive set theory）的影響，並討論了各種結果的 Borel 和一般類比。最後一章詳細介紹了 Gaboriau 最近在等價關係和群的成本理論上的結果，以及其在證明自由群作用的剛性定理中的應用。
