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Cambridge University Press
Table of Contents
Preface
1. Convex functions and sets
2. Orlicz spaces
3. Gauges and locally convex spaces
4. Separation theorems
5. Duality: dual topologies, bipolar sets, and Legendre transforms
6. Monotone and convex matrix functions
7. Loewner's theorem: a first proof
8. Extreme points and the Krein–Milman theorem
9. The strong Krein–Milman theorem
10. Choquet theory: existence
11. Choquet theory: uniqueness
12. Complex interpolation
13. The Brunn–Minkowski inequalities and log concave functions
14. Rearrangement inequalities: a) Brascamp–Lieb–Luttinger inequalities
15. Rearrangement inequalities: b) Majorization
16. The relative entropy
17. Notes
References
Author index
Subject index
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