Weak convergence of vector measures with applications to real analysis

矢量测量与实际分析应用的收敛性较弱

基本信息

批准号：
11640160
负责人：
KAWABE Jun
金额：
$ 1.28万
依托单位：
SHINSHU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640160/
关键词：
weak convergence injective tensor integral fuzzy optimization Fourier coefficients nonlinear regulator controller time-delay martingale-like sequence Riemannian submersion weak convergence of vector measures fuzzy set generalized Norlu

项目摘要

We have studied weak convergence of vector measures with values in Banach spaces and nuclear spaces, and have applied it to several interesting problems in real analysis, probability theory, control theory, differential geometry and so on. Some of our important results are as follows :1. By an essential use of Bartle's bilinear integration theory, it is shown that the injective tensor product of positive vector measures in certain Banach lattices is jointly continuous with respect to the weak convergence of vector measures.2. The weak compactness of a set of control inputs is shown in the case that they are given by the gravity calculation of time dependent fuzzy membership functions. As an application, the existence of optimal solution is discussed in a fuzzy control for an open-loop system.3. We obtain a convergence theorem of compound probability measures on a uniform space for a net of uniformly equicontinuous transition probabilities. This result applies to Gaussian transition probabilities on a Hilbert spaces.4. We obtain a general theorem for the method (N,p_n, q_n)(C, 1) summability of the sequence {nB_n (x)}, which contains some theorems due to S.P.Khare, V.K.Tripathi and A.N.Singh and et al.5. It is shown that some central manifold exists in a neighborhood of a point of equilibrium.6. It is shown that a set of fuzzy membership functions in the NBV space is compact with respect to the weak^* topology. This result applies to the existence of fuzzy optimal control.7. A relation between two convergence theorems of maritingale in the limit, i.e., L^1-boundedness and integrability of stopped processes is studied.8. We define another almost complex structure (resp.almost contact structure) and an indefinite Kahlerian (resp. Sasakian) manifold with affine connection.

我们已经研究了矢量测量与Banach空间和核空间中值的弱收敛性，并将其应用于真实分析，概率理论，控制理论，差异几何形状等的几个有趣问题。我们的一些重要结果如下：1。通过对Bartle双线性整合理论的必要用途，可以证明，对于某些Banach晶格中阳性矢量测量的张量张量对于矢量测量的弱收敛性是共同连续的。2。一组控制输入的弱紧凑性在通过重力计算的情况下给出了依赖时间的模糊成员函数。作为一种应用，在开环系统的模糊控制中讨论了最佳解决方案的存在。3。我们获得了均匀等效过渡概率净的均匀空间上复合概率度量的收敛定理。此结果适用于希尔伯特空间上的高斯过渡概率4。我们获得了方法（n，p_n，q_n）（c，1）序列{nb_n（x）}的总定理，该序列{nb_n（x）}，该序列包含由于s.p.khare，v.k.tripathi和a.n.singh和a.n.singh和et et.5而导致的一些定理。结果表明，某些中央流形存在于平衡点附近6。结果表明，相对于弱^*拓扑，NBV空间中的一组模糊成员函数是紧凑的。该结果适用于模糊最佳控制的存在7。研究了限制中的两个委托定理之间的关系，即l^1界限和止损过程的集成性。8。我们定义了另一种几乎复杂的结构（最大的接触结构）和具有仿射连接的无限kahlerian（sasakian）歧管。