On the Basic Representation Theorem for Convex Domination of Measures

A direct, constructive proof is given for the basic representation theorem for convex domination of measures. The proof is given in the finitistic case purely atomic measures with a finite number of atoms., and a simple argument is then given to extend this result to the general case, including both probability measures and finite Borel measures on infinite-dimensional spaces. The infinite-dimensional case follows quickly from the finite-dimensional case with the use of the approximation property.