Krein-Milman Theorem

The Krein-Milman Theorem states that in a locally convex topological vector space, a compact convex set equals the closed convex hull of its own extreme points, the points that cannot be written as a genuine average of two other points in the set. Named for Mark Krein and David Milman, it is a foundational result of functional analysis guaranteeing that a compact convex set is fully determined by its extreme points alone, with applications throughout convex analysis and optimization.