On almost uniform convergence theorems for the smallest semicopula-based universal integral

In this paper, we introduce a new property of a semicopula, called the uniform left (or right)-continuity in the first (or second) variable. Based on this new concept of continuity, a uniform convergence theorem for the smallest semicopula-based universal integral is given. In particular, a counter-...

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Bibliographic Details
Published in:Fuzzy sets and systems 2023-09, Vol.467, p.108592, Article 108592
Main Authors: Hoang, Do Huy, Son, Pham Thanh, Nhan, Truong Thi, Duc, Ho Quang, Duong, Dao Van
Format: Article
Language:English
Subjects:
Almost uniform convergence
Generalized measure theory
Monotone measure
Semicopula
The smallest semicopula-based universal integral
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Summary:In this paper, we introduce a new property of a semicopula, called the uniform left (or right)-continuity in the first (or second) variable. Based on this new concept of continuity, a uniform convergence theorem for the smallest semicopula-based universal integral is given. In particular, a counter-example is presented to show that Theorem 2.9 in Borzová-Molnárová et al. (2015) [4] is not true. Finally, some modified versions of Theorems 2.7, 2.8 and 2.9 in Borzová-Molnárová et al. (2015) [4] are studied.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2023.108592