On a sufficient condition of Lusin's theorem for non-additive measures that take values in an ordered topological vector space
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. (C) 2011 Published by Elsevier B.V.
lusin's theorem non-additive measure ordered vector space locally full topology