Weak convergence of nonadditive measures based on nonlinear integral functionals

作者：Kawabe Jun^*

来源：Fuzzy Sets and Systems, 2016, 289: 1-15.

DOI：10.1016/j.fss.2015.02.011

• Nonadditive measure
• Weak convergence of measures
• Choquet integral
• Sugeno integral
• Shilkret integral
• Integral functional
• Perturbation
• Portmanteau theorem

In this paper, we formulate a general portmanteau theorem for a perturbative nonlinear integral functional and discuss the uniformity of weak convergence of nonadditive measures based on such a functional. As their direct consequences, it turns out that Levy 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 applied when discussing the metrizability of the Levy topology on the space of nonadditive measures and defining the Fortet-Mourier type metrics on a uniformly equi-autocontinuous set of nonadditive measures.

• 出版日期2016-4-15