Analysis on Polish Spaces and an Introduction to Optimal Transportation

AvD. J. H. Garling

Inbunden, Engelska, 2017

Del 89 i serien London Mathematical Society Student Texts

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2017-12-21
Mått:157 x 235 x 24 mm
Vikt:620 g
Format:Inbunden
Språk:Engelska
Serie:London Mathematical Society Student Texts
Antal sidor:356
Förlag:Cambridge University Press
ISBN:9781108421577

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

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).

Recensioner i media

'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 Reviews

Innehållsförteckning

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. Càdlàg 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.