On Egoroff's theorems on finite monotone non-additive measure space

Authors:
Jun Li;Masami Yasuda
Affiliations:
Department of Applied Mathematics, College of Science, Communication University of China, Beijing 100024, People's Republic of China;Department of Mathematics & Informatics, Faculty of Science, Chiba University, Chiba 263-8522, Japan
Venue:
Fuzzy Sets and Systems
Year:
2005

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Abstract

In this note, we give four versions of Egoroff's theorem in non-additive measure theory by using condition (E), the pseudo-condition (E) of set function and the duality relations between the conditions. These conditions offered are not only sufficient but also necessary for the four kinds of Egoroff's theorems.