Relationship among continuity conditions and null-additivity conditions in non-additive measure theory

Authors:
Shin Asahina;Kenta Uchino;Toshiaki Murofushi
Affiliations:
Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan;Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan;Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan
Venue:
Fuzzy Sets and Systems
Year:
2006

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Abstract

The paper shows all the implication relationship among six continuity conditions and two null-additivity conditions with respect to non-additive measures. The six continuity conditions are continuity from above, order continuity, strong order continuity, exhaustivity, continuity from below, and null-continuity, and the two null-additivity conditions are null-additivity and weak null-additivity. The implication relationship is summarized in a diagram.