Analysis on Polish spaces and an introduction to optimal transportation
- D.J.H. Garling.
- Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2018.
- Copyright notice
- Physical description
- ix, 348 pages ; 23 cm.
- London Mathematical Society student texts ; 89.
At the library
Science Library (Li and Ma)
|QA611.28 .G36 2018||Unknown|
- Garling, D. J. H., author.
- Includes bibliographical references and index.
- Introduction-- Part I. Topological Properties:
- 1. General topology--
- 2. Metric spaces--
- 3. Polish spaces and compactness--
- 4. Semi-continuous functions--
- 5. Uniform spaces and topological groups--
- 6. C...dl...g functions--
- 7. Banach spaces--
- 8. Hilbert space--
- 9. The Hahn-Banach 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)
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)
- Publication date
- Copyright date
- London Mathematical Society student texts ; 89
- 9781108421577 hardcover ; alkaline paper
- 1108421571 hardcover ; alkaline paper
- 9781108431767 paperback ; alkaline paper
- 1108431763 paperback ; alkaline paper
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