Other Representation Theorems in Linear Spaces

Abstract

In this chapter, we shall prove three representation theorems in linear spaces. The first one, the Krein-Milman theorem says that a non-void convex compact subset K of a locally convex linear topological space is equal to the closure of the convex hull of the extremal points of K. The other two theorems concern the representations of a vector lattice as point functions and as set functions.