Topological Structure of Weak Convergence of Nonadditive Measures

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We introduced two explicit metrics for nonadditive measures on a metric space, which are called the Levy-Prokhorov metric and the Fortet-Mourier metric, and investigated their basic properties. Then, we gave a notion of the uniform equi-autocontinuity for a set of nonadditive measures and showed that both the Levy topology and the weak topology have uniform structures on such a set. As a result, we revealed that the Levy topology and the weak topology can be metrized by those explicit metrics.Next, we introduced an asymptotically translatable condition for a nonlinear functional to solve a Choquet integral representation problem for a comonotonically additive, monotone functional on the space of all continuous functions with compact support on a locally compact space.