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

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.