On almost uniform convergence theorems for the smallest semicopula-based universal integral. (English) Zbl 07898177
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 [J. Borzová-Molnárová et al., ibid. 271, 18–30 (2015; Zbl 1374.28026)] is not true. Finally, some modified versions of Theorems 2.7, 2.8 and 2.9 in [loc. cit.] are studied.
Keywords:
semicopula; monotone measure; almost uniform convergence; the smallest semicopula-based universal integral; generalized measure theoryCitations:
Zbl 1374.28026References:
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