A canonical definition of the joint semi-quantum operators of a finite family of random variables, having finite moments of all orders, is given first in terms of an existence and uniqueness theorem. Then two characterizations, one for the polynomially symmetric, and another for the polynomially factorizable probability measures, having finite moments of all orders, are presented.

中文翻译：

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用半量子算子表征概率测度

首先根据存在唯一性定理给出了具有所有阶的有限矩的有限随机变量族的联合半量子算子的规范定义。然后提出了两种表征，一种用于多项式对称，另一种用于多项式可分解概率测度，具有所有阶的有限矩。