I Representations of Points by Boundary Measures.- 1. Distinguished Classes of Functions on a Compact Convex Set.- 2. Weak Integrals, Moments and Barycenters.- 3. Comparison of Measures on a Compact Convex Set.- 4. Choquet's Theorem.- 5. Abstract Boundaries Defined by Cones of Functions.- 6. Unilateral Representation Theorems with Application to Simplicial Boundary Measures.- II Structure of Compact Convex Sets.- 1. Order-unit and Base-norm Spaces.- 2. Elementary Embedding Theorems.- 3. Choquet Simplexes.- 4. Bauer Simplexes and the Dirichlet Problem of the Extreme Boundary.- 5. Order Ideals, Faces, and Parts.- 6. Split-faces and Facial Topology.- 7. The Concept of Center for A(K).- 8. Existence and Uniqueness of Maximal Central Measures Representing Points of an Arbitrary Compact Convex Set.- References.
