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测度方法研究
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Let be a lattice of subsets of an abstract set .We assume φ∈.We call a content any non-negative set function μ defined on such that μ(φ)=0,ABμ(A)≤μ(B)and μ(A∪B)+μ(A∩B)= μ(A)+μ(B).For any A,we putand we set ={AΩ:DΩ,μ(D)=μ(D∩A)+μ(D∩A~c)}, ={AΩ:DΩ,μ(D)=μ(D∩A)+μ(D∩A~c)}, We obtein two following theorems,the second one generalizes a result given by Topsφs[3]. Theorem 3.1 If μ is a content on a lattice and continuous from below.Then 1)(Ω,,μ)is a complete measure space. BAμ(A)=μ(B)+μ(A\B). Theorem 3.2 If μ is a finite...

Let be a lattice of subsets of an abstract set .We assume φ∈.We call a content any non-negative set function μ defined on such that μ(φ)=0,ABμ(A)≤μ(B)and μ(A∪B)+μ(A∩B)= μ(A)+μ(B).For any A,we putand we set ={AΩ:DΩ,μ(D)=μ(D∩A)+μ(D∩A~c)}, ={AΩ:DΩ,μ(D)=μ(D∩A)+μ(D∩A~c)}, We obtein two following theorems,the second one generalizes a result given by Topsφs[3]. Theorem 3.1 If μ is a content on a lattice and continuous from below.Then 1)(Ω,,μ)is a complete measure space. BAμ(A)=μ(B)+μ(A\B). Theorem 3.2 If μ is a finite content on a lattice and continuous from above.Then 1)(Ω,,μ)is a complete measure space. 2)iff A,B∈,BAμ(A)=μ(B)+μ_*(A\B). Let be a π-class of subsets of Ω(i.e.A,B∈AB∈). We assume φ∈.If μ is an outer measure on in the sense that μ(φ)=0 and A,A_n∈,AA_nμ(A)≤μ(A_n). putting for AΩ μ°(A)=inf{μ(A_n):A_n∈@,AA_n}(infφ=+∞), then μ° is an outer measure on Ω in ordinary sense,so that(Ω,, μ°)is a complete measure space,where is defined .We have the following. Theorem 3.3.If μ is an outer measure on a π-class @.Then iff A,B∈,BAμ(A)=μ(B)+μ°(A\B).

设@为Ω上的一π类或格,本文用外测度及内测度方法研究了在什么条件下@上的一非负集函数可以扩张成为■(@)上的测度。这里■(@)={A■Ω:■C∈@,C∩A∈σ(@)},它是一σ代数,且包含由@生成的σ-代数σ(@)。主要结果是定理3.1、3.2及3.3.其中定理3.2推广了 Topsφe[3]及 Adamski[5]的一个结果。

In this paper, the method of vector measure is used to study the characteristics of dentable operator class and Radon-Nikodym operator class in Banach space. The results obtained are used to research into the structure of Banach space, giving out some new characteristics for Radon-Nikodym property of Banach space.

本文运用向量测度方法研究了Banach空问上可凹算子类与Radon-Nikodym算子类的特性,并把所得结果用于研究Banach空间的结构,给出Banach空间具有Randon-Nikodym性质的若干新特征。

In the paper, the theory of production frontiers and its non-parametric measurement ac Proaches are used to figure out the input compressing productivity index, Malmquist productivity index based on the input oriented non-parametric production frontiers. The technology efficiency and the distance function and their nonparametric models are introduced on the conditions of Constant Return to Scale and input strong disposability. The Non-parametric measurement approaches and the decomposition of Malmquist productivity...

In the paper, the theory of production frontiers and its non-parametric measurement ac Proaches are used to figure out the input compressing productivity index, Malmquist productivity index based on the input oriented non-parametric production frontiers. The technology efficiency and the distance function and their nonparametric models are introduced on the conditions of Constant Return to Scale and input strong disposability. The Non-parametric measurement approaches and the decomposition of Malmquist productivity index are put forward.

本文采用生产前沿面理论及其非参数方法,对假定产出确定条件下投入压缩的生产率指数──基于投入前沿面的Malmquist生产率指数进行了理论与测度方法研究。通过规模收益不变且要素自由(C,S)前沿面条件下的技术效率、距离函数及其非参数模型的分析,本文给出了基于非参数(C,S)投入前沿面的Malmquist生产率指数的非参数测度模型,并从技术变化和资源配置效率变化两个方面进行了分解。

 
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