Postprint version. Published in Journal of Mathematical Analysis and Applications, Volume 228, Issue 2, December 15, 1998, pages 449-466. Copyright © 1998 Elsevier. The definitive version is available at http://dx.doi.org/10.1006/jmaa.1998.6158.
NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.
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.