In this paper I discuss the relation between the concept of the Fisher metric and the concept of differentiability of a family of probability measures. I compare the concepts of smooth statistical manifolds, differentiable families of measures, $k$-integrable parameterized measure models, diffeological statistical models, differentiable measures, which arise in Information Geometry, mathematical statistics and measure theory, and discuss some related problems.

翻译：在本文中,我讨论了渔业计量概念与概率计量家庭可区别性概念之间的关系,我比较了在信息几何学、数学统计和计量理论中出现的光滑的统计多元、不同的计量家庭、可分类的参数计量模型、统计统计模型、可区分的计量方法等概念,并讨论了一些相关的问题。