Let X be a compact Hausdorff space and let A be a linear subspace of C(X; R) containing the constant functions, and separating points from probability measures. Then the inf-lattice generated by A is uniformly dense in C(X; R) . We show that this is a corollary of the Choquet-Deny Theorem, thus simplifying the proof and extending to the nonmetric case a result of McAfee and Reny.1211175178