Autocontinuity, strict convergence in measure and convergence of integral sequences

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.