局部凸分离空间上的Bartle积分  

Bartle Integral on a Locally Convex Separated Space

作　　者：乌仁其其格[1] 罗成[2] 

机构地区：[1]内蒙古赤峰学院数学学院,内蒙古赤峰024000 [2]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《内蒙古大学学报（自然科学版）》2012年第1期34-40,共7页Journal of Inner Mongolia University：Natural Science Edition

基　　金：内蒙古自然科学基金(No.200308020101)

摘　　要：提出了取值于局部凸空间的向量测度的p-变差与p-半变差的概念.设F是由Ω的子集作成的域,(X,σΡ)是局部凸分离空间,证明了从賦范空间到局部凸分离空间的有界线性算子的全体构成局部凸分离空间,有界的X值向量测度的全体也是局部凸分离空间.在局部凸分离空间为序列完备的前提下证明了以上两个空间拓扑同构,进而在局部凸分离空间上定义了Bartle积分,并把Banach空间上的关于向量测度的某些结论推广到了局部凸分离空间.p-variation and p-smivariation of vector measure valued in a locally convex separated space is introduced.Let F be a field of subsets of a set Ω,(X,σP)be a locally convex separated space.It is proved that the set of all bounded linear operators from a normed space to a locally convex separated space is a locally convex separated space.It is also proved that the set of all bounded vector measures valued in X is a locally convex separated space.With the precondition of locally convex separated space satisfy a sequence complete condition,the above-mentioned two spaces are isomorphic to each other.The Bartle integral on a locally convex separated space is defined.Moreovesome conclusions of vector measure on Banach space are generalized into a locally convex separated space.

关 键 词：局部凸分离空间 p-变差 p-半变差 向量测度 Bartle积分 

分 类 号：O177.99[理学—数学]