UID:
almahu_9947367871802882
Format:
1 online resource (441 p.)
ISBN:
1-281-79738-3
,
9786611797386
,
0-08-087167-4
Series Statement:
North-Holland mathematics studies ; 56
Content:
Convex Cones
Note:
Description based upon print version of record.
,
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
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2.4 Lattice Cones2.5 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
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2.3 Weak Dini Cones and Signed Representing Measures2.4 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
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5.1 Basic Definitions and their Meaning in the Classical Situation5.2 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
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A 2 MeasuresA 3 The Riesz Representation Theorem; A 4 The Radon-Nikodym Theorem; A 5 Signed and Lattice-valued Measures; REFERENCES; AUTHOR INDEX; SUBJECT INDEX
,
English
Additional Edition:
ISBN 0-444-86290-0
Language:
English
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