Compact convex sets and boundary integrals

Alfsen E.M.3540050906

Table of contents :
Title page ……Page 1
Series ……Page 3
Date-line ……Page 4
Preface ……Page 5
Contents ……Page 7
§1. Distinguished Classes of Functions on a Compact Convex Set ……Page 13
§2. Weak Integrals, Moments and Barycenters ……Page 21
§3. Comparison of Measures on a Compact Convex Set ……Page 33
§4. Choquet’s Theorem ……Page 43
§5. Abstract Boundaries Defined by Cones of Functions ……Page 56
§6. Unilateral Representation Theorems with Application to Simplicial Boundary Measures ……Page 67
§1. Order-unit and Base-norm Spaces ……Page 79
§2. Elementary Embedding Theorems ……Page 91
§3. Choquet Simplexes ……Page 96
§4. Bauer Simplexes and the Dirichlet Problem of the Extreme Boundary ……Page 115
§5. Order Ideals, Faces, and Parts ……Page 121
§6. Split-faces and Facial Topology ……Page 140
§7. The Concept of Center for $A(K)$ ……Page 165
§8. Existence and Uniqueness of Maximal Central Measures Representing Points of an Arbitrary Compact Convex Set ……Page 183
Appendix ……Page 201
References ……Page 205
Subject Index ……Page 221