Metrizability of the Lévy topology on the space of nonadditive measures on metric spaces

We formalize the Lévy–Prokhorov metric and the Fortet–Mourier metric for nonadditive measures on a metric space and show that the Lévy 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 Lévy 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.