概率分布的截度量
The cut metric for probability distributions
摘要：
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割度量的一个变形。除了建立基本的结果，我们引入了一个自然的操作称为{ \em钉扎}的空间上的限制对象，并显示如何产生一个典型的切割度量近似一个给定的概率分布类似于弱正则引理的graphons。我们还建立了割度量连续的基本操作，如采取积测度。
英文摘要：
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.
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