共查询到19条相似文献,搜索用时 130 毫秒
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在F-粗积分、■-粗积分定义的基础上研究了F-粗积分与■-粗积分之间的关系及粗变化度与粗萎缩度和粗扩充度、粗变化率与粗萎缩率和粗扩充率的关系。 相似文献
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利用变量代换、微分中值定理、积分几何意义、积分性质及夹逼定理、Γ -函数和β-函数关系等方法 ,对服从标准正态分布的随机变量 X ,其密度函数的概率积分公式 ,给出了多种证明方法 . 相似文献
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利用变量代换,微分中值定理,积分几何意义,积分性质及夹逼定理,Γ-函数和β-函数关系等方法,对服从标准正态分布的随机变量X,其密度函数的概率积分公式,给出了多种证明方法。 相似文献
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证明了随机赋范模中一个点是其任一子模的依概率范数的弱最佳逼近点当且仅当它是该子模的依概率范数的最佳逼近点,亦当且仅当该点是该子模的依随机范数的最佳逼近点.利用这些关系我们可以借助于随机赋范模的最近进展获得许多概率赋范空间中的新的最佳逼近定理. 相似文献
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函数单向S粗集对偶(dual offunction one direction singular rough sets)是函数S粗集的基本形式之一,函数单向S-粗集对偶具有动态特性与规律(函数)特性.函数S粗集(function singular rough sets)是把函数概念引入到S粗集内(singular rough sets)改进S粗集得到的把导数概念与函数单向S粗集对偶交叉、渗透给出粗边际规律F-粗边际规律概念;给出粗边际规律F-粗边际规律特征;给出F-粗边际规律与粗边际规律的关系;给出F-粗边际规律在经济信息系统中的应用 相似文献
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可测函数序列关于弱收敛概率测度序列积分的极限定理 总被引:1,自引:0,他引:1
研究了可测函数序列关于弱收敛概率测度序列积分的极限定理及其控制收敛定理,并给出了概率测度弱收敛的若干新的等价条件. 相似文献
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《数学物理学报(A辑)》2010,(6)
该文讨论了F-稳态映射的Liouville型定理,并证明了当初始流形的截面曲率满足某些非正条件、F满足F-p-条件时,具有有限F能量的F-稳态映射是常值映射.作者也研究了一类特殊的F-稳态映射,即服从积分F-守恒律的映射,并证明了一个类似的Liouville型定理,该定理的曲率假定和F-p-条件和上述定理相同,但F-能量有限性被替换成更弱的F-能量慢发散条件. 相似文献
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单调集函数的连续性与可测函数序列的收敛 总被引:3,自引:0,他引:3
引了单调集函数的几种连续性并且讨论了它们与可测函数依测度收敛之间的关系,给出可加测度论中的Lesbegue定理在单调测度空间上的4种推广形式。讨论单调集函数的连续性和模糊积分与Choquet积分的单调收敛定理之间的等价性。证明Choquet积分的控制收敛定理。 相似文献
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F-rough integrals is defined on the basis of the dual of function one direction S-rough sets,which has dynamic characteristics.Using F-rough integrals,the concepts of expansion measurement-expansion degree and expansion ratio are given.By expansion degree and expansion ratio the changing extent can be expressed with numbers,and the recognition principle of attribute effect on function equivalences is got. 相似文献
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R. N. Miroshin 《Mathematical Notes》2007,82(3-4):357-365
Multiple integrals generalizing the iterated kernels of integral operators are expressed as single integrals in the case of a special representation of the kernel (this is our theorem). Besides integral equations, Markov processes involve these integrals as well. As a consequence of the theorem, we obtain transition probability densities of certain Markov processes. As an illustration, we consider nine examples. 相似文献
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Michał Kisielewicz 《Journal of Mathematical Analysis and Applications》2012,388(2):984-995
The present paper is devoted to properties of set-valued stochastic integrals defined as some special type of set-valued random variables. In particular, it is shown that if the probability base is separable or probability measure is nonatomic then defined set-valued stochastic integrals can be represented by a sequence of Itô?s integrals of nonanticipative selectors of integrated set-valued processes. Immediately from Michael?s continuous selection theorem it follows that the indefinite set-valued stochastic integrals possess some continuous selections. The problem of integrably boundedness of set-valued stochastic integrals is considered. Some remarks dealing with stochastic differential inclusions are also given. 相似文献
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ConcerningaKindofintegralsofComplex-ValnedFunctionsofLargeNnmbersL.C.Hsu(Dept.ofMath.Sci.,DalianUniv.ofTech,Dalian110023)Conc... 相似文献
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Here presented are two limit theorems for a kind of integrals involvingcomplex-valued functions of large numbers. The form of integrals may be regardedas a natural generalization of those integrals occured in the probability limit theoremsof Chung and Erds. Our main result is Theorem 2 whose Proof rests upon some knownresults of [1] and makes an extentive use of Bonnet's second mean value theorem andrelated analytic techniques. 相似文献
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The present paper contains a martingale representation theorem for set-valued martingales defined on a filtered probability space with a filtration generated by a Brownian motion. It is proved that such type martingales can be defined by some generalized set-valued stochastic integrals with respect to a given Brownian motion. The main result of the paper is preceded by short part devoted to the definition and some properties of generalized set-valued stochastic integrals. 相似文献
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Let(Ω,Σ,μ)be a complete probability space and let X be a Banach space.We introduce the notion of scalar equi-convergence in measure which being applied to sequences of Pettis integrable functions generates a new convergence theorem.We also obtain a Vitali type I-convergence theorem for Pettis integrals where I is an ideal on N. 相似文献
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《数学学报》2014,(1)
<正>Vitali Type Convergence Theorems for Banach Space Valued Integrals Marek BALCERZAK Kazimierz MUSIAL Abstract Let(Ω,∑,μ)be a complete probability space and let X be a Banach space.We introduce the notion of scalar equi-convergence in measure which being applied to sequences of Pettis integrable functions generates a new convergence theorem.We also obtain a Vitali type I-convergence theorem for Pettis integrals where I is an ideal on N.On Universally Left-stability ofε-Isometry 相似文献
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Boris I. Golubov 《Analysis Mathematica》2006,32(3):173-205
Summary For the fractional dyadic derivative and integral, the following analogues of two theorems of Lebesgue are proved: the theorem
on differentiation of the indefinite Lebesgue integral of an integrable function at its Lebesgue points, and the theorem
on reconstruction of an absolutely continuous function by means of its derivative. Dyadic fractional analogues of the formula
of integration by parts are also obtained. In addition, some theorems are proved on dyadic fractional differentiation and
integration of a Lebesgue integral depending on a parameter. Most of the results are new even for dyadic derivatives and
integrals of natural order. 相似文献