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).
Inhaltsangabe
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.
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.
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