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In classical measure theory there are a number of convergence theorems, such as the Egorov, the Riesz and the Lusin theorem, among others. We consider monotone measures (i.e., monotone set functions vanishing in the empty set and defined on a measurable space) and discuss, how and to which extent classical convergence theorems can be carried over to this more general case.
In this paper, we answer the open question suggested by Wang et al. in ''Monotone set functions defined by Choquet integral'' (Fuzzy Sets and Systems 81 (1996) 241).
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