Set Sequences and Monotone Class
Bo Zhang, Hiroshi Yamazaki, Yatsuka Nakamura · 2005
Summary. In this paper we first defined the partial-union sequence, the partial-intersection sequence, and the partial-difference-union sequence of given sequence of subsets, and then proved the additive theorem of infinite sequences and sub-additive theorem of finite sequences for probability. Further, we defined the monotone class of families of subsets, and discussed the relations between the monotone class and the �-field which are generated by the field of subsets of a given set.