In this chapter, we study Information Geometry from a particular non-parametric or functional point of view. The basic model is a probabilities subset usually specified by regularity conditions. For example, probability measures mutually absolutely continuous or probability densities with a given degree of smoothness. We construct a manifold structure by giving an atlas of charts as mappings from probabilities to a Banach space. The charts we use are quite peculiar in that we consider only instances where the transition mappings are affine. We chose a particular expression of the tangent and cotangent bundles in this affine setting.

翻译：在本章中，我们从特定的非参数或泛函视角研究信息几何。基本模型是一个通常由正则性条件定义的概率子集。例如，相互绝对连续的概率测度或具有给定光滑度的概率密度函数。我们通过建立从概率空间到Banach空间的图册映射来构造流形结构。我们所采用的图册具有特殊性——仅考虑转移映射为仿射的情形。在此仿射框架下，我们选择了切丛与余切丛的特定表达形式。