单调测度空间上集值函数的Lebesgue定理

The Lebesgue Convergence Theorems of Measurable Closed-valued Functions

本文利用单调集函数的4种连续性的定义和可测函数序列的4种收敛性之间的关系,提出了4种类型的Lebesgue定理,并给出了单调集函数在空集连续,全集连续的充要条件。

With four continuity of non - additive set function and the relation of four convergences of the measurable function sequence, four forms Lebesgue theorem about measurable closed - valued functions on monotone measure space are discussed, respectively . And the sufficient and necessary conditions of the monotone set function which is continuous of the empty set and the full set are given.