Chentsov's theorem

Chentsov's theorem is a result in the field of information geometry and statistics, particularly related to the study of statistical manifolds and the structure of probability distributions. It states that any smooth statistical manifold (which is a differentiable manifold modeling a family of probability distributions) can be equipped with a Riemannian metric that reflects the underlying geometry of the probability distributions. The theorem is particularly important in establishing a connection between statistical estimation, geometry, and information theory.