In 1944, von Neumann and Morgenstern raised a question in their famous book Theory of Games and Economic Behavior: For a rational agent with preferences over all probabilistic mixtures of finitely many deterministic outcomes, is there always a unique utility function on deterministic outcomes whose expected value on probabilistic mixtures represents the preferences? Under natural assumptions on the preference order, they answered the question positively. We attempt to generalize this result to the case when the outcomes are infinite. We first identify the outcomes with the extreme points of a Choquet simplex, a natural generalization of the classical simplex to infinite-dimensional spaces. We then prove a similar result in the setting of Choquet simplex.