Isomorphism of borel full groups
Isomorphism of borel full groups
复制标题
Borel满群同构
DOI：
10.1090/s0002-9939-06-08542-x
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发表时间：
2006
影响因子：
1.2
通讯作者：
Christian Rosendal
中科院分区：
文献类型：
--
作者：
B. D. Miller;Christian Rosendal
设G和H是在Polish空间X和Y上以Borel方式作用的Polish群，E_G^X和E_H^Y表示相应的轨道等价关系，[G]和[H]表示相应的Borel满群。对明显的反例取模，我们证明了[G]≅[H]⇔E_G^X≅_B E_H^Y
Suppose that G and H are Polish groups which act in a Borel fashion on Polish spaces X and Y. Let E_G^X and E_H^Y denote the corresponding orbit equivalence relations, and [G] and [H] the corresponding Borel full groups. Modulo the obvious counterexamples, we show that [G] ≅ [H] ⇔ E_G^X ≅_B E_H^Y