THE LEVY-PROKHOROV TOPOLOGY ON NONADDITIVE MEASURES ON METRIC SPACES (Mathematical Studies on Independence and Dependence Structure : Algebra meets Probability)
Jun Kawabe · Kyoto University Research Information Repository (Kyoto University) · 2012
We formalize the L\'evy-Prokhorov metric and the Fortet-Mourier metric for nonadditive measures on a metric space and show that the L\'evy $top$ ol- ogy on every uniformly equi-autocontinuous set of Radon nonadditive measures can be metrized by such metrics.This result is proved using the uniformity for L\'evy 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.