一句话：用多重集和范畴论建立无元素概率分布理论，并给出交换随机划分与随机分布的表示定理。
在贝叶斯统计中，概率分布所赋值的元素有时仅充当标签，其具体身份并不重要；忘记这些元素后剩下的结构即为“无元素”概率分布。本文用多重集与范畴论发展其结构理论，给出在无元素分布与普通分布之间转换的操作，并证明这些操作与多项采样交换。基于此，作者证明两个表示定理：无元素分布可为贝叶斯非参数聚类中的两类关键随机结构提供自然表示——可交换随机划分，以及由基测度参数化的随机分布。
An "element-free" probability distribution is what remains of a probability distribution after we forget the elements to which the probabilities were assigned. These objects naturally arise in Bayesian statistics, in situations where elements are used as labels and their specific identity is not important. This paper develops the structural theory of element-free distributions, using multisets and category theory. We give operations for moving between element-free and ordinary distributions, and we show that these operations commute with multinomial sampling. We then exploit this theory to prove two representation theorems. These theorems show that element-free distributions provide a natural representation for key random structures in Bayesian nonparametric clustering: exchangeable random partitions, and random distributions parametrized by a base measure.