Graphings are special bounded-degree graphs on probability spaces, representing limits of graph sequences that are convergent in a local or local-global sense. A graphing is compact, if the underlying space is a compact metric space, the edge set is closed and nearby points have nearby graph neighborhoods. We prove some simple properties of compact graphings. Our main result is a procedure for embedding an arbitrary graphing into an essentially equivalent compact graphing.

中文翻译：

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紧凑的图形

图形是概率空间上的特殊有界度图，表示在局部或局部全局意义上收敛的图序列的极限。一个图形是紧凑的，如果底层空间是一个紧凑的度量空间，边集是封闭的并且附近的点有附近的图邻域。我们证明了紧凑图形的一些简单属性。我们的主要结果是将任意图形嵌入到本质上等效的紧凑图形中的过程。