Countable abelian group actions and hyperfinite equivalence relations
成果类型：
Article
署名作者：
Gao, Su; Jackson, Steve
署名单位：
University of North Texas System; University of North Texas Denton
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-015-0603-y
发表日期：
2015
页码：
309-383
关键词：
摘要：
An equivalence relation E on a standard Borel space is hyperfinite if E is the increasing union of countably many Borel equivalence relations where all -equivalence classs are finite. In this article we establish the following theorem: if a countable abelian group acts on a standard Borel space in a Borel manner then the orbit equivalence relation is hyperfinite. The proof uses constructions and analysis of Borel marker sets and regions in the space This technique is also applied to a problem of finding Borel chromatic numbers for invariant Borel subspaces of .
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