Analysis on Polish Spaces and an Introduction to Optimal Transportation

Nonfiction, Science & Nature, Mathematics, Topology, Mathematical Analysis
Cover of the book Analysis on Polish Spaces and an Introduction to Optimal Transportation by D. J. H. Garling, Cambridge University Press
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Author: D. J. H. Garling ISBN: 9781108381956
Publisher: Cambridge University Press Publication: December 21, 2017
Imprint: Cambridge University Press Language: English
Author: D. J. H. Garling
ISBN: 9781108381956
Publisher: Cambridge University Press
Publication: December 21, 2017
Imprint: Cambridge University Press
Language: English

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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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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