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In this paper, we give a necessary and sufficient condition to guarantee that the space of all finite measurable functions for a monotonic measure is a topological vector space with a countable local base and in this space convergence with respect to this topology is equivalent to the convergence in measure.
In this paper, we discuss the inheriting of convergence of the monotonic measures under the following operations: addition, multiplication, max and min and the uniqueness of convergence of a monotonic measure. Moreover, we also point out that autocontinuity from above cannot imply double asymptotic null-additivity for monotonic measures using a counterexample contrary to the case of fuzzy measures...
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