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Fuzzy regular measures on topological spaces. (English) Zbl 0983.28009
Summary: The concepts of the inner regularity, outer regularity and regularity of a fuzzy measure are introduced on a topological space, their properties are studied in detail and Egoroff’s theorem and Lusin’s theorem are proved. Finally, the conditions for a fuzzy measure to be tight and perfect are given, respectively.

28E10Fuzzy measure theory
54A40Fuzzy topology
Full Text: DOI
[1] R. Engelking, General Topology, Warszawa, 1977.
[2] Ha, M.; Wang, X.: Some notes on the regularity of fuzzy measures on metric spaces. Fuzzy sets and systems 87, 385-387 (1997) · Zbl 0933.28008
[3] Halmos, P. R.: Measure theory. (1962)
[4] Jiang, Q.; Suzuki, H.: Fuzzy measures on metric spaces. Fuzzy sets and systems 83, 99-106 (1996) · Zbl 0878.28013
[5] Parthasarathy, K. R.: Probability measures on metric spaces. (1967) · Zbl 0153.19101
[6] Wu, C.; Ha, M.: On the regularity of the fuzzy measure on metric fuzzy measure spaces. Fuzzy sets and systems 66, 373-379 (1994) · Zbl 0844.28009