Regularity and Lusin's theorem for Riesz space-valued fuzzy measures

Authors:
Jun Kawabe
Affiliations:
Department of Mathematics, Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

A smoothness condition (the multiple Egoroff property) is introduced and imposed on a Riesz space to show that every weakly null-additive, Riesz space-valued fuzzy Borel measure on any metric space is regular. It is also proved that Lusin's theorem remains valid for such Riesz space-valued non-additive measures.