We formalize the Levy-Prokhorov metric and the Fortet-Mourier metric for nonadditive measures on a metric space and show that the Levy topology on every uniformly equi-autocontinuous set of Radon nonadditive measures can be metrized by such metrics. This result is proved using the uniformity for Levy convergence on a bounded subset of Lipschitz functions. We describe some applications to stochastic convergence of a sequence of measurable mappings on a nonadditive measure space.