چکیده (انگلیسی):

In this paper, we formulate a general portmanteau theorem for a perturbative nonlinear integral functional and discuss the unifor-mity of weak convergence of nonadditive measures based on such a functional. As their direct consequences, it turns out that Lévy convergence of nonadditive measures coincides with every one of three types of weak convergence, that is, weak Choquet, weak Sugeno, and weak Shilkret convergence and they are uniform on every bounded subset of Lipschitz functions. Those results are ap-plied when discussing the metrizability of the Lévy topology on the space of nonadditive measures and defining the Fortet–Mourier type metrics on a uniformly equi-autocontinuous set of nonadditive measures.