Analysis on Polish Spaces and an Introduction to Optimal Transportatio

Detailed account of analysis on Polish spaces with a straightforward introduction to optimal transportation.

List of contents

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.

About the author

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).

Summary

This detailed account of analysis on Polish spaces contains results that apply to probability theory and a gentle introduction to optimal transportation. Containing more than 200 elementary exercises, it is a useful resource for advanced mathematical students and also for researchers in mathematical analysis.

Product details

• Authors: D. J. H. Garling, D. J. H. (University of Cambridge) Garling, Garling D. J. H.
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 31.12.2017
• EAN: 9781108421577
• ISBN: 978-1-108-42157-7
• No. of pages: 356
• Series: London Mathematical Society Student Texts; London Mathematical Society St; London Mathematical Society Student Texts
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Basic principles; MATHEMATICS / Mathematical Analysis, Calculus & mathematical analysis, Calculus and mathematical analysis