类切饼集上测度的局部维数存在的充要条件

本文研究了类切饼集上有限Borel正则测度的局部维数性质.利用中值定理和有界畸变原理,获得了一类类切饼集上测度的局部维数存在的一个充要条件,所获结果包含了已有结果.     

切测度的几何分析

本文研究了Radon测度μ的切测度,给出了切测度的Rectifiability.利用对偶性原理及Blow-up 技巧证明了连续函数的微切集的存在性.另外,本文给出了切测度的平坦性特征.作为切测度的应用, 证明了Marstrand定理.     

切测度的几何分析

本文研究了Radon测度μ的切测度,给出了切测度的Rectifiability.利用对偶性原理及Blow-up技巧证明了连续函数的微切集的存在性.另外,本文给出了切测度的平坦性特征.作为切测度的应用,证明了Marstrand定理.     

距离空间上测度正则性的推广

本文给出了单调类与σ代数关系的充要条件,进一步得出距离空间的开集全体产生的最小单调类与产生的σ代数相等.利用这关系,证明了距离空间上的σ-有限测度也是正则测度.推广了距离空间上有限测度的正则性.     

集值测度的RadOn-Nikodym定理及集值算子的Pettis-Aumanri积分表示

本文建立了Banach空间集值测度的Radon-Nikodym定理,并给出了两类集值算子的Pettis-Aumann积分表示.     

随机测度的绝对连续性与相互奇异性

§1.定义与问题 恒设(X,d)是可分完备距离空间.(?)表示X上的Borel集类(开集产生的σ代数).以(?)记(?)中全体有界集组成的集类. 显然(?)是一环,但当X不是有界距离空间时,(?)就不是σ环。虽然(?)不是σ环,但对任意A∈(?),A∩(?)是σ代数. . 设μ是(X,(?))上的测度,如对任意A∈(?),μ(A)<+∞.则称μ是局部有限测度.     

有界闭凸值测度的集值积分

引入实值函数关于有界闭凸值测度的集值积分,并讨论了集值积分的收敛定理,证明了当集值测度为有界闭凸集值的有界变差集值测度时,关于弱紧凸集值测度的积分性质对有界闭凸集值测度仍然保持.推广了实值函数关于弱紧凸值测度的积分.     

集值测度的表示定理

1972年,Z.V.Artstein研究了集值测度的基本性质,得到了选择定理、凸性定理等.本文给出了集值测度的表示定理.证明了任何一族一致有界、两两等比的测度可以生成一个有界闭凸集值测度.同时,证明了有界闭凸集值测度可以找到它的一族一致有界选择,使得这族选择生成这个集值测度本身.     

新序意义下集值模糊测度的伪自连续性

在m维正欧式空间的子集类上, 通过引入集合的新序和依序收敛的概念,讨论新序意义下集值模糊测度的伪自连续、一致伪自连续性,并研究它们的蕴涵关系,从而丰富集值模糊测度的理论.     

拟相似集的Hausdorff测度的特征

Siegfried GRAF在文献［1］中给出了自相似集上的Hausdorff测度(简称H-测度)的特征.John McLaughlin在文献［2］中引入了拟相似集的概念,K.J.Falconer又在文献［3］中讨论了拟相似集上H-测度和维数的性质.本文研究拟相似集上的H-测度的特征,并得出在一定条件下支撑于其上满足一定条件的测度与H-测度的等价性条件.     

分数布朗桥测度及其分部积分公式

In this paper, we focus on the characterization for fractional Brownian bridge measures. We give the integration by parts formula for such measures by Bismut''s method and their pull back formula. Conversely, we prove that such measures can be determined through their integration by parts formula.     

集值测度的收敛性及其与Castaing向量表示中测度的收敛性之间的关系

本文研究了集值测度的收敛性. 利用极限理论的方法,在X有RNP,且M(∪)s-lim inf_(n→∞) M_n条件下,获得了集值测度的收敛性与其 Castaing表示中向量测度收敛性的关系,建立了集值测度列与集值测度选择列的收敛性,从而对进一步研究集值测度的一些件质提供了理论依据.     

A generalization of local divergence measures

In this paper we propose a generalization of the concept of the local property for divergence measures. These new measures will be called g-local divergence measures, and we study some of their properties. Once this family is defined, a characterization based on Ling’s theorem is given. From this result, we obtain the general form of g-local divergence measures as a function of the divergence in each element of the reference set; this study is divided in three parts according to the cardinality of the reference set: finite, infinite countable or non-countable. Finally, we study the problem of componible divergence measures as a dual concept of g-local divergence measures.     

A generalization of local divergence measures

In this paper we propose a generalization of the concept of the local property for divergence measures. These new measures will be called g-local divergence measures, and we study some of their properties. Once this family is defined, a characterization based on Ling’s theorem is given. From this result, we obtain the general form of g-local divergence measures as a function of the divergence in each element of the reference set; this study is divided in three parts according to the cardinality of the reference set: finite, infinite countable or non-countable. Finally, we study the problem of componible divergence measures as a dual concept of g-local divergence measures.     

H-值半鞅测度的弱收敛

本文引进了H-值半鞅测度，研究了其基本性质和与之相联系的随机积分，本文还引入了H-值半鞅测度序列依分布弱收敛的概念，建立了H-值半鞅测度的极限定理，给出了H-值半鞅测度弱收敛的条件。     

Lattice measures and associated outer measures

In this paper, we consider lattice measures and introduce certain associated outer measures (not the usual induced outer measures), study their properties, and investigate the associated classes of measureable sets. We utilize some of these outer measures to characterize normality and investigate lattice separation properties; also, to extend the notion of regularity of measures to weak regularity of measures. We give applications of our results to specific topological lattices.     

The Frobenius traces distribution for modular Abelian surfaces

We prove that there exist at least 15 pairs of measures for which the two normalized Frobenius traces on modular Abelian surfaces are equidistributed. Under an assumption about stochastic independence, we prove that there are exactly 18 such pairs of measures. Moreover, we describe all of them by giving their moments and distributions.     

Statistical experiments and their conical measures

Summary In the theory of functional analytic comparison of statistical experiments (started by L. LeCam) one can characterize equivalence classes of experiments by conical measures (in the sense of G. Choquet). We begin with a short proof of the (known) fact that any conical measure with normed resultant belongs to an experiment class. Then we are concerned with the special case of dominated experiments which are characterized by the extendability of their conical measures to finite concrete measures. These results are in close connection with a paper of E.N. Torgersen (Mixtures and products of dominated experiments. Ann. Statist. 5, 44–64 (1977)).After this we study class properties of experiments which are expressible in terms of their conical measures. Simple examples are domination, existence of bounded densities and compactness. It follows the investigation of a more profound class property which we call extremality and which generalizes the concept of an experiment with a sufficient and boundedly complete subalgebra. Finally we prove that the extreme points of the compact convex set of conical measures with normed resultant are just the conical measures of the extremal experiments.     

Extreme points of some families of non-additive measures

Non-additive measures are a valuable tool to model many different problems arising in real situations. However, two important difficulties appear in their practical use: the complexity of the measures and their identification from sample data. For the first problem, additional conditions are imposed, leading to different subfamilies of non-additive measures. Related to the second point, in this paper we study the set of vertices of some families of non-additive measures, namely k-additive measures and p-symmetric measures. These extreme points are necessary in order to properly apply a new method of identification of non-additive measures based on genetic algorithms, whose cross-over operator is the convex combination. We solve the problem through techniques of Linear Programming.     

Cumulative measures of information and stochastic orders

In this paper we present some known results on cumulative measures of information, study their properties and relate these definitions to concepts of reliability theory. We give some relations of these measures of discrimination with some well-known stochastic orders and with the relative reversed hazard rate order. We investigate also a stochastic comparison among the empirical cumulative measures that can be related to the cumulative measures. Large part of this paper is a survey article; however, in the last section, we define a new measure of discrimination between residual lifetimes and study some of its properties.