单调集函数的连续性与可测函数序列的收敛

Continuity of Monotone Set Function and Convergences of Measurable Function Sequence

引了单调集函数的几种连续性并且讨论了它们与可测函数依测度收敛之间的关系,给出可加测度论中的Lesbegue定理在单调测度空间上的4种推广形式。讨论单调集函数的连续性和模糊积分与Choquet积分的单调收敛定理之间的等价性。证明Choquet积分的控制收敛定理。

In this paper, different kinds of continuity of monotone set function are introduced and four forms of generalization on monotone measure space for Lebesgue＇s theorem are presented, respectively. The equivalence among the continuity from below and above of monotone set function, and the monotone convergence theorems of fuzzy and of Choquet integral are discussed, respectively. Dominated convergence theorem of Choquet integral is shown.