Notes on Riesz's theorem on fuzzy measure space
Fuzzy Sets and Systems
Fundamental convergence of sequences of measurable functions on fuzzy measure space
Fuzzy Sets and Systems
Fuzzy Measure Theory
Pseudo-atoms of fuzzy and non-fuzzy measures
Fuzzy Sets and Systems
On Egoroff's theorems on finite monotone non-additive measure space
Fuzzy Sets and Systems
On the space of measurable functions and its topology determined by the Choquet integral
International Journal of Approximate Reasoning
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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 proved by Ha et al. [Fundamental convergence of sequences of measurable functions on fuzzy measure space, Fuzzy Sets and Systems 95 (1998) 77-81]. Finally, we show that for monotonic measure convergence, double asymptotic null-additivity is better than autocontinuity from above.