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Autocontinuity, strict convergence in measure and convergence of integral sequences

  • Do Huy Hoang , Truong Thi Nhan , Dao Van Duong und Tran Nhat Luan ORCID logo EMAIL logo
Veröffentlicht/Copyright: 29. August 2025
Journal of Applied Analysis
Aus der Zeitschrift Journal of Applied Analysis

Abstract

In this paper, we give an alternative proof for the proof of Theorem 2.23 shown in the paper [J. Borzová-Molnárová, L. Halčinová and O. Hutník, The smallest semicopula-based universal integrals II: Convergence theorems, Fuzzy Sets and Systems 271 2015, 18–30] by exploiting the uniform continuity of the underlying semicopula together with using ε-techniques of limit. Thus, our proof avoids using the way interchanging the supremum and infimum which is not valid in general.

References

[1] J. Borzová-Molnárová, L. Halčinová and O. Hutník, The smallest semicopula-based universal integrals II: Convergence theorems, Fuzzy Sets and Systems 271 (2015), 18–30. 10.1016/j.fss.2014.09.024Suche in Google Scholar

[2] J. Borzová-Molnárová, L. Halčinová and O. Hutník, The smallest semicopula-based universal integrals: Remarks and improvements, Fuzzy Sets and Systems 393 (2020), 29–52. 10.1016/j.fss.2019.05.010Suche in Google Scholar

[3] D. H. Hoang, P. T. Son, H. Q. Duc, D. Van Duong and T. N. Luan, On a convergence in measure theorem for the seminormed and semiconormed fuzzy integrals, Fuzzy Sets and Systems 457 (2023), 156–168. 10.1016/j.fss.2022.08.008Suche in Google Scholar

[4] D. H. Hoang, P. T. Son, T. T. Nhan, H. Q. Duc and D. V. Duong, On almost uniform convergence theorems for the smallest semicopula-based universal integral, Fuzzy Sets and Systems 467 (2023), Article ID 108592. 10.1016/j.fss.2023.108592Suche in Google Scholar

[5] J. Li, R. Mesiar, E. Pap and E. P. Klement, Convergence theorems for monotone measures, Fuzzy Sets and Systems 281 (2015), 103–127. 10.1016/j.fss.2015.05.017Suche in Google Scholar

[6] X. C. Liu, Further discussion on convergence theorems for seminormed fuzzy integrals and semiconormed fuzzy integrals, Fuzzy Sets and Systems 55 (1993), no. 2, 219–226. 10.1016/0165-0114(93)90134-4Suche in Google Scholar

[7] T. N. Luan, D. H. Hoang, T. M. Thuyet, H. N. Phuoc and K. H. Dung, A note on the smallest semicopula-based universal integral and an application, Fuzzy Sets and Systems 430 (2022), 88–101. 10.1016/j.fss.2021.07.005Suche in Google Scholar

[8] F. Suárez García and P. Gil Álvarez, Two families of fuzzy integrals, Fuzzy Sets and Systems 18 (1986), no. 1, 67–81. 10.1016/0165-0114(86)90028-XSuche in Google Scholar

Received: 2025-04-17
Revised: 2025-07-21
Accepted: 2025-07-27
Published Online: 2025-08-29

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 21.11.2025 von https://www.degruyterbrill.com/document/doi/10.1515/jaa-2025-0047/html?lang=de
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