Ay N., Jost J., Lê H.V., Schwachhöfer L. Information Geometry

Springer International Publishing AG, 2017. — 411 p. — (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics 64) — ISBN: 3319564773.The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional.-Introduction
-Finite Information Geometry
-Parametrized Measure Models
-The Intrinsic Geometry of Statistical Models
-Information Geometry and Statistics
-Fields of Application of Information Geometry
Appendixes
Measure Theory
Riemannian Geometry
Banach Manifolds