SIAM Journal on Discrete Mathematics, Volume 35, Issue 2, Page 1096-1135, January 2021.
Guided by the theory of graph limits, we investigate a variant of the cut metric for limit objects of sequences of discrete probability distributions. Apart from establishing basic results, we introduce a natural operation called pinning on the space of limit objects and show how this operation yields a canonical cut metric approximation to a given probability distribution akin to the weak regularity lemma for graphons. We also establish the cut metric continuity of basic operations such as taking product measures.

中文翻译：

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概率分布的切割度量

SIAM Journal on Discrete Mathematics，第 35 卷，第 2 期，第 1096-1135 页，2021 年 1 月
。在图极限理论的指导下，我们研究了离散概率分布序列的极限对象的切割度量的变体。除了建立基本结果之外，我们还介绍了一种称为限制对象空间上的固定的自然操作，并展示了该操作如何产生对给定概率分布的规范割度量近似，类似于图形子的弱正则性引理。我们还建立了基本操作的切割指标连续性，例如采取产品措施。