On a sufficient condition of Lusin's theorem for non-additive measures that take values in an ordered topological vector space

Authors:
Toshikazu Watanabe;Toshiharu Kawasaki;Tamaki Tanaka
Affiliations:
Graduate School of Science and Technology, Niigata University, 8050, Ikarashi 2-no-cho, Nishi-ku, Niigata 950-2181, Japan;Graduate School of Science and Technology, Niigata University, 8050, Ikarashi 2-no-cho, Nishi-ku, Niigata 950-2181, Japan;Graduate School of Science and Technology, Niigata University, 8050, Ikarashi 2-no-cho, Nishi-ku, Niigata 950-2181, Japan
Venue:
Fuzzy Sets and Systems
Year:
2012

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Abstract

Classical Lusin's theorem is extended for real-valued fuzzy measures under the weak null-additivity condition recently. In this paper, we show similar results for non-additive measures that take values in an ordered topological vector space. Firstly, we prove Lusin type theorem for weakly null-additive Borel measures that are continuous from above and possess an additional continuity property suggested by Sun in 1994. Secondly, we state another one for weakly null-additive fuzzy Borel measures. Our results are applicable to several ordered topological vector spaces.