Regularity and Lusin's theorem for Riesz space-valued fuzzy measures
In non-additive measure theory, \textit{J. Li} and \textit{M. Yasuda} [Fuzzy Sets Syst. 146, No. 1, 121--133 (2004; Zbl 1046.28012)] proved that every weakly null-additive fuzzy Borel measure on a metric space is regular and Lusin's theorem remains valid for such non-additive measures. The purpose of this paper is to extend those results to Riesz space-valued fuzzy measures. Instead of epsilon-argument, a smoothness condition (the multiple Egoroff property) on a Riesz space is introduced and imposed to show this regularity property. Then, by using this regularity and Egoroff's theorem, it is also proved that Lusin's theorem remains valid.
scientific article; zbMATH DE number 5149486