The authors study the purification of measure-valued maps. In the main theorem they study measurable mappings from a nonatomic Loeb probability space to the space of Borel probability measures on a compact metric space. They show that for a measurable mapping \(f\) between the spaces one can find a measurable mapping \(g\) between the spaces such that \(f\) and \(g\) yield the same values for the integrals associated with a countable class of functions between the spaces. As corollaries they obtain results that generalize the classical Dvoretzky-Wald-Wolfwitz theorem. They also deduce certain other interesting and useful results.