4.7 Article

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

期刊

FUZZY SETS AND SYSTEMS
卷 430, 期 -, 页码 174-179

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ELSEVIER
DOI: 10.1016/j.fss.2021.09.012

关键词

Monotone set-valued measure; Regularity; Egoroff's theorem

资金

  1. Fundamental Research Funds for the Central Universities (in Communication University of China) [CUC2000006]

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This note points out the invalidity of a theorem and the defects in two proofs in a paper, and raises an open problem regarding the characteristics of monotone measures.
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. (c) 2021 Elsevier B.V. All rights reserved.

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