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Considerations on (Pseudo-) Convergences of Sequences of Measurable Functions on Monotone Set Multifunction Space In this paper, we further a previous study concerning convergences and pseudo-convergences of sequences of measurable functions on monotone set multifunction spaces. Various considerations concerning operations and the uniqueness of the limit with respect to such convergences are given and several asymptotic structural properties of certain set multifunctions are, in this way, characterized.