Autocontinuity is a necessary and sufficient condition for convergence in measure of fuzzy integrals in sequences of measurable functions, suggesting improved understanding of integral behavior.
The key result in this paper shows that autocontinuity is a sufficient and necessary condition on a monotone measure such that convergence in measure of a sequence of measurable functions implies convergence of the corresponding sequence of seminormed fuzzy integrals of those measurable functions. Our work is an improvement of several previously published results.
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Hoang et al. (2026) studied this question.
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