发表机构
KU Leuven; University of Münster（荷语鲁汶大学; 明斯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究为可数可测群胚引入正则近距概念，证明其与关联冯·诺依曼代数的强化相对正则近距等价，探究其持久性并确定多类正则近距群胚，同时证明内可和群胚不具备该性质。
AI 中文摘要
我们为可数可测群胚引入正则近距（proper proximality）的概念，将可数群的对应概念进行推广。我们证明该群胚性质等价于其关联的群胚冯·诺依曼代数的强化型相对正则近距性质。我们研究其持久性性质，特别表明正则近距在有限直积、变换群胚构造及测度等价下保持。我们还确定了大类正则近距群胚，包括横截可测群胚和自由积群胚，并证明内可和群胚永远不是正则近距的。
英文摘要
We introduce the notion of proper proximality for countable measured groupoids, extending the corresponding notion for countable groups. We prove that this groupoid property is equivalent to a strengthened form of relative proper proximality for the associated groupoid von Neumann algebra. We investigate permanence properties and show, in particular, that proper proximality is preserved under finite direct products, formation of transformation groupoids, and measure equivalence. We also identify broad classes of properly proximal groupoids, including transverse measured groupoids and free product groupoids, and prove that inner amenable groupoids are never properly proximal.
