Analysis on Polish spaces and an introduction to optimal transportation
著者
書誌事項
Analysis on Polish spaces and an introduction to optimal transportation
（London Mathematical Society student texts, 89）
Cambridge University Press, 2018
- : hardback
- : pbk
大学図書館所蔵 全18件
注記
Includes bibliographical references (p. 339-341) and index
内容説明・目次
内容説明
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.
目次
- 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. Cadlag 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.
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