单调可测集合列外测度极限的性质及其应用  

Properties Related to the Limitation of Exterior Measure of a Monotonous Measurable Set Sequence and Its Applications

作　　者：唐建国[1] 

机构地区：[1]惠州学院数学与大数据学院,广东惠州516007

出　　处：《惠州学院学报》2016年第6期10-13,18,共5页Journal of Huizhou University

基　　金：广东省人才引进资金项目(A410.0204);惠州学院科研项目(C511.0211)

摘　　要：本文将外测度的有限可加性推广为外测度的可数可加性,紧接着利用它推导出递增可测集合列外测度极限的一个重要性质,对于递减可测集合列外测度的极限也有类似的性质.从这些性质出发,我们容易证明递增、递减、收敛及一般可测集合列测度极限的一系列重要结果,此时一列可测集合的并与交可测是其简单推论.In this paper; we generalize the finite additive property of exterior measure to the countable and additive property of exterior measure ; and then we deduce an important property related to the limitation of exterior measure of an increasing set sequence by using it. For a decreasing set sequence ; there is a similar property related to the limitation of exterior measure. From these properties ; we can easily prove a series of important results related to limitations of the measure of increasing; decreasing; convergence and general measur- able set sequences. At this time ; it is simple corollaries that union and intersection of a measurable set sequence are also measurable set.

关 键 词：外测度 测度 可数可加性 可测集列 极限 

分 类 号：O174.1[理学—数学]