Analysis on Polish Spaces and an Introduction to Optimal Transportation

A large part of mathematical analysis both pure and applied takes place on Polish spaces: topological spaces whose topology can be given by a complete metric. This analysis is not only simpler than in the general case but more crucially contains many important special results. This book provides a detailed account of analysis and measure theory on Polish spaces including results about spaces of probability measures. Containing more than 200 elementary exercises it will be a useful resource for advanced mathematical students and also for researchers in mathematical analysis. The book also includes a straightforward and gentle introduction to the theory of optimal transportation illustrating just how many of the results established earlier in the book play an essential role in the theory.