广义可加Fuzzy测度的Radon—Nikodym定理

本文在[1,2]的基础上证明了广义可加fuzzy测度的Radon-Nikodym定理和Lebes-gue分解定理,从而完善了可加fuzzy测度的理论。     

面积定理推广

本文把单位国外ｍ叶半纯函数的面积定理，推广到只假定函数在无穷有ｍ级极点情形．并给出面积大于零的充要条件．     

集值Vitali-Hahn-Saks-Nikodym定理

本文通过强可加集值测度的一个等价叙述引入集值测度一致强可加的概念,并建立了集值测度的Vitali-Hahn-Saks-Nikodym定理.     

关于外测度极限定理的证明的两点注记

实例说明关于外测度极限定理的个别证明存在不妥之处 ,而由外测度基本性质及其它可补证该定理     

Banach空间上集值测度与模糊数测度的扩张

在Banach空间上,给出集值测度的扩张定理并借助集测度的扩张给出了模糊数测度的扩张定理。     

条件数学期望的几何定义及其应用

给出随机变量关于一般σ代数的条件数学期望的几何定义,利用高等代数中投影定理可证明该定义与经典条件数学期望定义的一致性.     

Cookie-Cutter~集上的~Gibbs~测度

Cookie-Cutter集不仅是动力系统中重要的研究对象,而且是分形中一类重要的集合.而支撑在其上的Gibbs测度对计算分形维数和热力学机制的熵起关键性作用.本文借助于定理2.1构造了支撑在其上的Gibbs测度,并用遍历性证明了该测度的唯一性.     

迭代函数系统的遍历性质—Elton定理的改进

本文改进Elton定理的结论,得到迭代函数系统的几个新的遍历定理。     

实变函数反例研究(Ⅱ)

列举了实变函数中的多个反例.这些反例说明,在条件改变之后一些重要结论不再成立.这可增强人们对实变函数内容的深刻认识.文中的测度与积分都不是Lebesgue测度与积分.     

On the associativity of the product of measure spaces

If we arbitrarily choose finitely many measure spaces, then the existence of a product of these measure spaces can be proved. It is well known that this operation is not associative which is a substantial difficulty. In this paper we show that the associative law remains true between the σ-algebras of the product spaces, and we give an extension of the Fubini's theorem. This revised version was published online in June 2006 with corrections to the Cover Date.     

Vitali定理的一个注记

证明了Vitali定理的部分逆定理成立,从而给出了函数列依测度收敛的一个充分必要条件。     

通过反复无限细分定义测度

This paper generalizes the method of constructing measure by repeated finite subdivision in fractal geometry to that by infinite subdivision. Two conditions for the existing method are removed. A measure on the interval [0,1] is constructed using this generalized method.     

Convexity Theorem for Subharmonic Functions with Respect to the Kolmogorov Operator

In this note, a version of the classical Riesz theorem for convexity of mean of subharmonic function on a annulus is given for the Kolmogorov's operator. Further, potential theoretical interpretations of a `mean value measure' are listed. Mathematics Subject Classifications (2000): 31B35, 31C05, 31C15.     

Four counterexamples to the Fubini theorem

In this paper we study signed measures. Our main results are as follows: the Fubini theorem is not true in the general case; the Jordan parts of a transition measure are not necessarily transition measures; the operation of taking the Jordan parts does not necessarily commute with multiplying by the initial measure; the product of σ-bounded measures need not be a σ-bounded measure. Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 124–127, July, 1997. Translated by S. S. Anisov     

On the Alexandroff decomposition theorem

We prove an Alexandroff decomposition type theorem, which extends a decomposition theorem proved in [de LUCIA, P.—MORALES, P.: Decomposition of group-valued measures in orthoalgebras, Fund. Math. 158 (1998), 109–124].      

关于Hausdorff测度的一个不等式

设F是R2中的子集,则下列不等式成立Hs(F)Bs(F)(2 33)sHs(F)其中s=d imH(F),Bs(F)如(6)式中所定义.