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σ代数
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  σ algebra
     FUZZY σ ALGEBRA AND FUZZY MEASURE
     弗晰σ——代数与弗晰测度
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  相似匹配句对
     X, σ?
     X、σ?
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     Fuzzifying sigma algebra and It's Properties
     模糊化σ-代数及性质
     Y, and σ?
     Y和σ?
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     Fisher Information Quantity and Sufficient σ-algebra
     Fisher信息量和充分性σ-代数
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     CONDITIONAL INDEPENDENCE OF σ-ALGEBRA VARIETY
     σ代数族的条件独立性
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  σ algebra
A logicoalgebraic approach to the geometry of Lagrangian systems is pursued by starting axiomatically with a classical mechanical system whose logic is a separable and atomic Boolean σ algebra.
      
The logicoalgebraic foundations of the Lagrangian and Hamiltonian techniques of contact mechanics are exhibited, by starting axiomatically with a classical system whose logic is a Booleanσ algebra.
      
Following the idea of Zadeh, the concept of a statistical (or fuzzy)σ algebra is introduced.
      


The Purpose of this paper is to define a generalized martingale and to discuss its Convergency.we have studied the existence of right-closed element and its relation to Some Convergency;an upcros- sing inequality to generalize Doob's Convergence theorem Concerning martingale and Serni-martingale;and introduced the generalized Potential,for proving the new decomposition theorem.

本文目的在于定义一种广义鞅并且讨论它的收敛性.文中首先给出了与某个增加的σ—代数族适应的随机序列几乎必然收敛的充分条件,推广了 J.L.Doob 的鞅收敛定理.然后讨论了广义鞅具有广义右闭元的条件以及它和几种收敛性之间的关系.最后叙述并且证明了广义鞅的 Riesz 型分解定理.

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, a valid application by FM Embedding Representation Theorem is described First, using an embedding operator, which is in fact the Radon-Nikodym derivative of signed measures, and under the simple condition, we can build the general representation theorem for F-entropy tropy on a common F-algebra and for a monotone weakly continuous F-entropy d(·).Then,the existence theorem in [2] can be extended from the normal F-measure space to a common F-measure space. Finally, many forms of fuzzy quasi-entropy...

In this paper, a valid application by FM Embedding Representation Theorem is described First, using an embedding operator, which is in fact the Radon-Nikodym derivative of signed measures, and under the simple condition, we can build the general representation theorem for F-entropy tropy on a common F-algebra and for a monotone weakly continuous F-entropy d(·).Then,the existence theorem in [2] can be extended from the normal F-measure space to a common F-measure space. Finally, many forms of fuzzy quasi-entropy can be discussed.

本文是FM嵌入表示定理的有效应用之一。我们利用广义测度的Radon—Nikodym导数,这嵌入算子(?)和简单的∑~*条件,在普通的F-σ-代数σ上,对仅是单调弱连续的F-熵d(·)建立了一般性的F-熵表示定理,确定了一般的F-熵的具体积分形式;然后。把[2]文的存在定理从正规的F∑—测度空间推广到普通的F-测度空间。并且讨论了缺乏保序赋值性的F-熵的多种形式。

 
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