Analysis on Polish spaces and an introduction to optimal transportation
 Responsibility
 D.J.H. Garling.
 Publication
 Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2018.
 Copyright notice
 ©2018
 Physical description
 ix, 348 pages ; 23 cm.
 Series
 London Mathematical Society student texts ; 89.
At the library
Science Library (Li and Ma)
Stacks
Call number  Status 

QA611.28 .G36 2018  Unknown 
More options
Description
Creators/Contributors
 Author/Creator
 Garling, D. J. H., author.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Introduction Part I. Topological Properties:
 1. General topology
 2. Metric spaces
 3. Polish spaces and compactness
 4. Semicontinuous functions
 5. Uniform spaces and topological groups
 6. C...dl...g functions
 7. Banach spaces
 8. Hilbert space
 9. The HahnBanach theorem
 10. Convex functions
 11. Subdifferentials and the legendre transform
 12. Compact convex Polish spaces
 13. Some fixed point theorems Part II. Measures on Polish Spaces:
 14. Abstract measure theory
 15. Further measure theory
 16. Borel measures
 17. Measures on Euclidean space
 18. Convergence of measures
 19. Introduction to Choquet theory Part III. Introduction to Optimal Transportation:
 20. Optimal transportation
 21. Wasserstein metrics
 22. Some examples Further reading Index.
 (source: Nielsen Book Data)
 Summary

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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2018
 Copyright date
 2018
 Series
 London Mathematical Society student texts ; 89
 ISBN
 9781108421577 hardcover ; alkaline paper
 1108421571 hardcover ; alkaline paper
 9781108431767 paperback ; alkaline paper
 1108431763 paperback ; alkaline paper
 9781108383875