重分形Hausdorff测度的有限测度子集

设μ为 Ｒ^d上 Ｂｏｒｅｌ概率测度,ｑ,ｔ∈Ｒ,记 Ｈ_μ^q,t为 Ｏｌｓｅｎ定义的重分形 Ｈａｕｓｄｏｒｆｆ测度,证明了当μ为测度时,Ｈ_μ^q,t的有限测度子集存在．     

关于s－维Hausdorff测度的注记

本完善了s-维Hausdorff测度当s＝0时的一种定义形式，证明了修改后的定义与另外几种定义方式的等价性，从而得出结论：不同献中对应于不同定义方式的结论是一致的。     

Operator-decomposability of Gaussian measures on separable Banach spaces

An operator-decomposable Gaussian measure on a separable Banach space can be factorized into a convolution product of a strongly operator-decomposable Gaussian measure and an operator-invariant Gaussian measure (with respect to the same operator). An example for this very factorization is discussed in some detail. In particular it is shown that a strongly operator-decomposable Gaussian measure need not necessarily be supported by the contraction subspace of the operator involved. Finally, the decomposability semigroup of a Gaussian measure turns out to be convex; and the corresponding invariance semigroup belongs to its extreme boundary.     

Notes on Riesz''s theorem on fuzzy measure space

Riesz's theorems on fuzzy measure space have been improved in essence.     

The exact measures of a class of self-similar sets on the plane

Let S (C) R2 be the attractor of the iterated function system{f1,f2,f3}iterating on the unit equilateral triangle So,where fi(x)=λix bi,I=1,2,3,x=(x1,x2),b1=(0,0),62=(1-λ2,0),63=(1-λ3/2,√3/2(1-λ3)).This paper determines the exact Hausdorff measure,centred covering measure and packing measure of S under some conditions relating to the ontraction parameter.     

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 possibility measure is not a fuzzy measure

In this note we show that a possibility measure is not a particular type of fuzzy measure, except in trivial cases.     

Comparison of fractal measures

In this paper, the relationship between the s-dimensional Hausdorff measures and the g-measures in Rd is discussed, where g is a gauge function which is equivalent to ts and 0 < s≤d. It shows that if s=d, then Hg = c1Hd, Cg = c2Cd and Pg = c3Pd on Rd, where constants c1, c2 and c3 are determined by where Wg, Cg and Pg are the g-Hausdorff, g-central Hausdorff and g-packing measures on Rd respectively. In the case 0相似文献   

Equivalent σ-finite invariant measures

Given a non-singular transformation T on a σ-finite measure space (X,β,m), we describe a new ratio condition that is necessary and sufficient for the existence of a T-invariant σ-finite measure equivalent to m.     

DOUBLING MEASURES ON GENERALIZED CANTOR SETS

We study the doubling property of binomial measures on generalized ternary Cantor subsets of [0, 1]. We find some new phenomena. There are three different cases. In the first case, we obtain an equivalent condition for the measure to be doubling. In the other cases, we show that the condition is not necessary. Then facts and partial results are discussed.     

Second derivatives of convex functions in the sense of A. D. Aleksandrov on infinite-dimensional spaces with measure

We consider convex functions on infinite-dimensional spaces equipped with measures. Our main results give some estimates of the first and second derivatives of a convex function, where second derivatives are considered from two different points of view: as point functions and as measures.     

Derived random measures

A derived random measure is constructed by integration of a random process with respect to a random measure independent of that process. Basic distributional properties, a continuity theorem, sample path properties, a strong law of large numbers, and a central limit theorem for derived random measures are established. Applications are given to compounding and thinning of point processes and the measure of a random set.     

Lebesgue测度等测包及其应用

利用Lebesgue测度的等测内核和等测外包讨论内外测度的一系列性质,给出外测度有限可加的一个充要条件,该条件改进了原有外测度有限可加性相关问题的结果.     

一类广义Sierpinski海绵的填充测度

对于m2的任何整数m,本文定义了R~m中的一类广义 Sierpinski海绵,同时给出了该类海绵的填充测度的计算公式.     

Continuous transformation of Baire measures into Lebesgue measure

A recent result by Wulbert on the existence of continuous functions with measure zero level sets is slightly extended and its proof is considerably simplified. As a by-product, a criterion is established for a Baire measure to allow a continuous transformation into Lebesgue measure.

     

Contributions to a Rigidity Conjecture

Let p and q be two relatively prime positive integers and a Borel probability measure invariant and ergodic by the semigroup generated by the action of both zp and zq. We analyse sufficient conditions to guarantee that is either the Lebesgue measure or supported on a periodic orbit. And extend the results for general expanding differentiable maps of the circle.     

Measures on finite concrete logics

We examine the possibility to extend measures and signed measures on a concrete logic on a finite set to those on all its subsets.