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 {\em 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.

翻译：在图形限制理论的指导下,我们调查了限制离散概率分布序列物体的削减指标的变体。除了确定基本结果外,我们还在限制物体空间上引入了一种称为 ~ em pinning} 的自然操作, 并展示这种操作如何产生一种卡通截线近似于像软硬石图的常规性列马的某种概率分布。 我们还建立了基本操作的削减指标连续性, 如采取产品措施。