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.
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