Analysis on Polish Spaces and an Introduction to Optimal Transportation
Published on 21. December 2017
Book
Hardback
356 pages
978-1-108-42157-7 (ISBN)
Description
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.
Reviews / Votes
'This book provides a detailed and concise account of analysis and measure theory on Polish spaces, including results about probability measures. Containing more than 200 elementary exercises, it will be a useful resource for advanced mathematical students and also for researchers in analysis.' Luca Granieri, Mathematical ReviewsMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 2 Line drawings, black and white
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 26 mm
Weight
735 gr
ISBN-13
978-1-108-42157-7 (9781108421577)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
E-Book
12/2017
Cambridge University Press
€42.99
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E-Book
12/2017
Cambridge University Press
€35.49
Available for download
Book
12/2017
Cambridge University Press
€61.90
Shipment within 15-20 days
Person
D. J. H. Garling is a Fellow of St John's College, Cambridge, and Emeritus Reader in Mathematical Analysis at the University of Cambridge. He has written several books on mathematics, including Inequalities: A Journey into Linear Algebra (Cambridge, 2007) and A Course in Mathematical Analysis (Cambridge, 2013).
Content
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.