In this paper we consider a concept of statistical causality, based on Granger’s definition of causality and analyze the relationships between given causality and the concept of measurable separability of $\sigma$-algebras. The measurable separability of $\sigma$-algebras is defined in Florens et al. (1990). We give a generalization of that definition for flows of information represented by filtrations and consider some properties of measurable separability that are directly connected to the concept of statistical causality. Also, we apply some of these results on Bayesian experiment.

中文翻译：

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统计因果关系和可测量的可分离性 $\sigma$-代数

在本文中，我们考虑了统计因果关系的概念，基于格兰杰对因果关系的定义，并分析了给定因果关系与可测量可分离性概念之间的关系。 $\sigma$-代数。可测量的可分离性$\sigma$-algebras 在 Florens 等人中定义。(1990)。我们对由过滤表示的信息流的定义进行了概括，并考虑了与统计因果关系概念直接相关的可测量可分离性的一些属性。此外，我们将其中一些结果应用于贝叶斯实验。