Elsevier

Fuzzy Sets and Systems

Volume 194, 1 May 2012, Pages 66-75
Fuzzy Sets and Systems

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

https://doi.org/10.1016/j.fss.2011.09.010Get rights and content

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.

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