向量值测度的泛函表示  

A Functional Characterization of Vector-valued Measures

作　　者：施慧华[1] 

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《厦门大学学报（自然科学版）》2013年第3期306-308,共3页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金专项数学天元基金项目(11226129);华侨大学高层次人才科研启动基金项目(10BS215)

摘　　要：给定有限测度空间(Ω,A,μ),令MX(A)=span{∑ni=1=χAixi,Ai∈A,xi∈X,n∈N}L∞(μ,X).证明了(Ω,A)上的向量值有限可加测度m是可列可加的当且仅当其对应泛函U是w*-序列连续的,对应关系由U(x)=∫Ωdm(x∈MX(A))确定.并借助于向量值测度的Yosida-Hewitt分解定理,进一步证明了任一定义于MX(A)上的连续线性泛函均能唯一分解成w*序列连续泛函与纯连续泛函的l和.For a finite measure space （（Ω,A,μ）,let Mx（A） be the space of the uniform limits of the form ∑χ_Ai x_i （finite sum） withA, A_i∈A and xi∈ X. In this paper we show that a sufficient and necessary condition for a finitely additive vector-valued measure m on（Ω,A）to be countably additive is that the corresponding functional U defined by U（x） = ∫Ωx Jdm （for x∈Mx（A）） is w＊ -sequentiallycontinuous. With help of the Yosida-Hewitt decomposition theorem of vector-valued case,we show consequently that every continu-ous linear functional on Mx （A） can be uniquely decomposed into the 11-sum of a w＊-sequentially continuous functional and a purely continuous functional.

关 键 词：向量值测度 泛函表示 测度分解 w＊-序列连续 

分 类 号：O177[理学—数学]