Book contents
- Frontmatter
- 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, I. Brascamp–Lieb–Luttinger inequalities
- 15 Rearrangement inequalities, II. Majorization
- 16 The relative entropy
- 17 Notes
- References
- Author index
- Subject index
Subject index
Published online by Cambridge University Press: 01 June 2011
- Frontmatter
- 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, I. Brascamp–Lieb–Luttinger inequalities
- 15 Rearrangement inequalities, II. Majorization
- 16 The relative entropy
- 17 Notes
- References
- Author index
- Subject index
Summary
- Type
- Chapter
- Information
- ConvexityAn Analytic Viewpoint, pp. 343 - 345Publisher: Cambridge University PressPrint publication year: 2011