Choquet Theory in Metric Spaces
Copyright policy )Choquet Theory in Metric Spaces
This paper deals with a generalization of the classical Choquet theorem. We consider metric spaces which are endowed with an abstract notion of convexity. Convex combinations are obtained by the solutions of variational inequalities. A generalized Krein-Milman theorem is derived from our Choquet theorem. We end with an example based on hyperbolic geometry.
- TU Dresden Germany
Convex functions and convex programs in convex geometry, Convex sets in topological linear spaces; Choquet theory, Spherical and hyperbolic convexity, Choquet theorem, Inequalities and extremum problems involving convexity in convex geometry, metric structure, convex subsets, Variants of convex sets (star-shaped, (\(m, n\))-convex, etc.), extreme points, Convex sets in topological vector spaces (aspects of convex geometry)
Convex functions and convex programs in convex geometry, Convex sets in topological linear spaces; Choquet theory, Spherical and hyperbolic convexity, Choquet theorem, Inequalities and extremum problems involving convexity in convex geometry, metric structure, convex subsets, Variants of convex sets (star-shaped, (\(m, n\))-convex, etc.), extreme points, Convex sets in topological vector spaces (aspects of convex geometry)
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