Choquet theory

Summary

Choquet theory studies how a point of a compact convex set is an average of its extreme points. The average is taken with respect to a probability measure on the set, called a representing measure. It refines the Krein–Milman theorem, which only says that the set is the closed convex hull of its extreme points. The theory applies to sets of measures, of states and of positive functions, where extreme points are the simplest objects.