Some properties of the variations of non-additive set functions I

✍ Scribed by Qiang Zhang

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 123 KB
• Volume: 118
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(98)00422-9

✦ Synopsis

The disjoint variation and chain variation in classical measure theory play an important role in the decompositions of signed measures, where they coincide. But they are usually di erent for non-additive set functions. In this paper, we discuss some properties of the variations, such as, the (null-) null-additivity, exhaustivity, order continuity, continuity and so on. A version of the Jordan decomposition theorem is proved for signed lower semicontinuous fuzzy measures.