We introduce inner amenability for discrete probability-measure-preserving (p.m.p.) groupoids and investigate its basic properties, examples, and the connection with central sequences in the full group of the groupoid or central sequences in the von Neumann algebra associated with the groupoid. Among other things, we show that every free ergodic p.m.p. compact action of an inner amenable group gives rise to an inner amenable orbit equivalence relation. We also obtain an analogous result for compact extensions of equivalence relations that either are stable or have a nontrivial central sequence in their full group.

中文翻译：

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内在顺从的 GROUPOIDS 和中心序列

我们介绍了离散概率测度保留 (pmp) 群的内在顺应性，并研究了它的基本性质、示例以及与群群的完整群中的中心序列或与群群相关的冯诺依曼代数中的中心序列的联系。除其他外，我们证明了内部服从群的每个自由遍历 pmp 紧致动作都会产生内部服从轨道等价关系。我们还为等价关系的紧凑扩展获得了类似的结果，这些关系要么是稳定的，要么在其整个组中具有非平凡的中心序列。