弱收敛序列

First, we present various new convergence concepts for sequence of fuzzy random variables, including convergence sure, convergence almost sure, uniform convergence, uniform convergence almost sure, almost uniform convergence, convergence in chance measure, and their corresponding weak convergence. Second, the relations among some types of convergence are studied. Finally, we design some algorithms about fuzzy random simulations to compute the mean chance of fuzzy random event, find the optimistic value of a return function, and evaluate the expected value of a fuzzy random variable.

首先，提出了几类模糊随机变量序列的收敛性概念，包括：必然收敛、几乎必然收敛、一致收敛、几乎必然一致收敛、近一致收敛、依机会测度收敛以及与以上概念相对应的弱收敛；其次，讨论了收敛性之间的关系；最后我们设计了模糊随机模拟算法，用于计算模糊随机事件的平均机会，寻找收益函数的乐观值，以及估计模糊随机变量的期望值。

First, we present various new convergence concepts for sequence of fuzzy random variables, including convergence sure, convergence almost sure, uniform convergence, uniform convergence almost sure, almost uniform convergence, convergence in chance measure, and their corresponding weak convergence.

首先，提出了几类模糊随机变量序列的收敛性概念，包括：必然收敛、几乎必然收敛、一致收敛、几乎必然一致收敛、近一致收敛、依机会测度收敛以及与以上概念相对应的弱收敛；其次，讨论了收敛性之间的关系；最后我们设计了模糊随机模拟算法，用于计算模糊随机事件的平均机会，寻找收益函数的乐观值，以及估计模糊随机变量的期望值。

It investigates mainly the dualinvariant of λ- multiplier convergent series, the full invariant ofλ-multiplier convergent series, the λ- multiplier convergent series in spaceswith a basis, the compact sets in the infinite matrix topological algebras, thecharacteristics of have the same compact sets in different topologies,the weak sequentially completeness of , the characteristics ofSchur-matrices, the characteristics of p- uniform Toeplitz matrices and theEberlein-Smulian theorem in the locally convex spaces, etc.

主要研究了〓数乘收敛级数的对偶不变性，〓数乘收敛级数的全程不变性，有基空间中的〓数乘收敛级数，无穷矩阵拓扑代数〓中的紧集，〓在不同拓扑下具有相同紧集的刻划，〓的弱序列完备性，Schur—矩阵的刻划，p-一致Toeplitz矩阵的刻划以及局部凸空间上的Eberlein—Smulian定理等。

With four continuity of non-additive set function and the relation of four convergences of the measurable function sequence,four forms Lebesgue theorem about measurable closed-valued functions on monotone measure space are discussed,respectively.

在经典测度论中，Lebesgue定理刻画了实值可测函数序列几乎处处收敛和依测度收敛之间的关系。1984~1986年，王震源[9]先后提出了较弱的"自连续"、"零可加"、"伪自连续"、"伪零可加"等重要概念，讨论了模糊测度空间上单值可测函数序列各种收敛之间的关系，推广了经典测度论中著名的Lebesgue定理以及其他定理。

Limit theorems for the integration of function sequence with respect to weak convergence probability measure sequence are proved under the condition of the weak tight, which have been used to research the some convergence of expectant functional sequence,and a sufficient condition for the epi-convergence of expectant functional sequence is obtained.

提出了弱胎紧的概念，并在弱胎紧的条件下证明了函数序列关于弱收敛概率测度序列积分的极限定理，用其研究了期望泛函序列的若干收敛性，得到了期望泛函序列的、上图收敛的一个充分条件。

The variational convergence of real function sequence is extended to vector function sequence and the lower semicontinuity of approximating set of weak Pareto solutions of a given multiobjective decision making problem with general constraint set is obtained by using the variational convergence.

本文将函数序列的v－收敛性推广到向量值函数，在v－收敛性的条件下得到了给定的多目标决策问题的近似弱有效解集的下半连续性并给出了若干容易验证的充分条件。

This paper,uses the property of being uniformly integrable to truncate the random variable sequences,and under the condition of φx↑,φx2↓,obtain a weak law of large number of martingale difference sequences by the weak convergence theorem.

通过使用一致收敛性对随机变量序列进行截尾，并借助随机变量序列的弱收敛定理，在φ↑，φx2↓的条件下给出了一个鞅差序列的弱大数定律。

In the first chapter, we used the method of majoring sequences to studied the convergences of Newton s methods of " reducing the counting of derivative" and "without inversing of derivative under weak conditions".

在第一章中，用优序列方法研究了减少导映照计值次数和避免导映照求逆的牛顿迭代在弱条件下的收敛性。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。