The Inclusion Variation of Non-additive Set Functions on T-Tribe

Inclusion variation on T_infin-tribe play an important role in T_infin-measures and fuzzy games theory, where they were used for additive set functions on T_infin-tribe. In this paper classical variations theory is extended to non-additive set functions on T-tribe, after defining the inclusion variation, we investigate its some properties in detailed, such as, the (null-) null-additivity, exhaustivity, order continuity, continuity from the left and so on. As to the inclusion variation on T_infin-tribe, an alternative proof of the Jordan decomposition theorem is given. Some relative results about inclusion variation in classical measure theory are generalized.