Property A introduced by Guoliang Yu is an amenability-type property for metric spaces. In this article, we study property A for uniformly locally finite coarse spaces. Main examples of coarse spaces are a metric space, a set equipped with a discrete group action, and a sequence of finitely generated groups. The purpose of this article is to give complete proofs to related basic theorems.

中文翻译：

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粗糙空间的属性 A

于国良介绍的性质A是度量空间的顺应性性质。在本文中，我们研究均匀局部有限粗空间的性质 A。粗空间的主要例子是度量空间、配备离散群动作的集合和有限生成群的序列。本文的目的是对相关的基本定理给出完整的证明。