Convex Cones
Published on 18. August 2011
428 pages
978-0-08-087167-7 (ISBN)
Description
Convex Cones
More details
Other editions
Additional editions
B. Fuchssteiner | W. Lusky
Convex Cones: Volume 56
Book
04/2000
North-Holland
€185.70
Article exhausted; check different version
Content
- Front Cover
- Convex Cones
- Copyright Page
- TABLE OF CONTENTS
- PREFACE
- CHAPTER I: LINEAR FUNCTIONALS
- Chapter I.1. The Sandwich Theorem
- 1.1 Semi groups
- 1.2 Cones
- 1.3 Some Consequences of the Sandwich Theorem
- 1.4 Sum Theorem and Finite Decomposition Theorem
- 1.5 Some elementary Applications
- 1.6 The Riesz-König Theorem
- 1.7 A Strassen-type Disintegration Theorem
- 1.8 Some Applications
- 1.9 Additional Remarks and Comments
- Chapter I.2 Order Units and Lattice Cones
- 2.1 Order Unit Cones
- 2.2 The Kakutani-Krein-Stone-Yosida Theorem
- 2.3 Order Complete Vector Lattices with Order Unit
- 2.4 Lattice Cones
- 2.5 Riesz Property and Finite Sum Property
- 2.6 The Positive Dual Cone
- 2.7 Dual Orders and the Cartier-Fell -Meyer Theorem
- 2.8 Free Lattice Cones
- 2.9 Simplicia1 Cones
- 2.10 Characters
- 2.11 Some Examples
- 2.12 Remarks and Comments
- CHAPTER II: REPRESENTING MEASURES
- Chapter II.1 Countable Decomposition
- 1.1 Preliminaries
- 1.2 The Main Decomposition Theorems
- 1.3 Dini Cones
- 1.4 Weak Dini Cones
- 1.5 Remarks and Comments
- Chapter II.2 Representing Measures
- 2.1 Decomposition Properties and Measure Theory
- 2.2 Dini Cones and Representing Measures
- 2.3 Weak Dini Cones and Signed Representing Measures
- 2.4 Representing Measures on Weighted Cones
- 2.5 Dirichlet States
- 2.6 Elementary Examples and Applications
- 2.7 Remarks and Comments
- Chapter II.3 Boundaries
- 3.1 Fixpoint Boundaries, Bauer's Maximum Principle and the Krein-Milman Theorem
- 3.2 More Boundaries
- 3.3 Choquet's Theorem
- 3.4 Maximal Measures
- 3.5 The Choquet-Meyer Theorem
- 3.6 Dini Boundaries
- 3.7 Remarks and Comments
- Chapter II.4 Integral Representation of Operators taking Values in an Order Complete Vector Lattice
- Chapter II.5 Generalized Hewitt-Nachbin Spaces
- 5.1 Basic Definitions and their Meaning in the Classical Situation
- 5.2 The F- Compactification
- 5.3 The F- Realcompactification
- 5.4 F- Pseudocompactness
- 5.5 Some Consequences
- 5.6 Remarks and Comments
- Chapter II.6 Examples and Applications
- 6.1 Completely Monotonic Functions
- 6.2 Kendall ' s Theorem on Infinitely Divisible Completely Monotonic Function
- 6.3 Multiplicative Cones
- 6.4 Banach Algebras and Spectral Theory
- 6.5 The Bochner-Weil Theorem
- 6.6 The Lévy-Khintchine Formula
- 6.7 Remarks and Comments
- APPENDIX: Measures and the Riesz Representation Theorem
- A 1 s- Algebras
- A 2 Measures
- A 3 The Riesz Representation Theorem
- A 4 The Radon-Nikodym Theorem
- A 5 Signed and Lattice-valued Measures
- REFERENCES
- AUTHOR INDEX
- SUBJECT INDEX
