The Egoroff property and the Egoroff theorem in Riesz space-valued non-additive measure theory

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

The Egoroff theorem remains valid for any Riesz space-valued non-additive measure which is strong order continuous and possesses a form of continuity called ''property (S)'' in the literature, whenever the Riesz space has the Egoroff property. This version of the Egoroff theorem is also valid for any non-additive measure with the property of uniform autocontinuity, strong order continuity and continuity from below by assuming only the weak @s-distributivity which is weaker than the Egoroff property.