Some notes on monotone set-valued measures and Egoroff's theorem

Abstract In this note, we point out that Theorem 3 (a version of Egoroff's theorem for monotone set-valued measures) shown in the paper “Lusin's theorem for monotone set-valued measures on topological spaces” (Fuzzy Sets and Systems 364 (2019) 111-123) is not valid, and we present two revised versions. We also point out that the proofs of Lemma 2 and Theorem 1 are defective, thus the truth of their conclusions cannot be affirmed. Thereby, an open problem for the characteristics of monotone measures is raised.