测度论

在证明过程中，我们也顺便得到测度论中Hahn分解定理的推广。

As a by-product of our proof , a new generalization of Hahn decomposition theorem in measure theory is obtained .

测度论中实值积分理论的推广

Popularization of Real-Valued Integral Theory in Measure Theory

经典测度论中所涉及到的集函数是满足可加性要求的，Hahn分解理论是很重要的定理。

As we know , classical ( signed ) measure is a set function which is additive . Hahn decomposition theorem is very important .

第二章介绍了分析中的Fourier级数，测度论基础中的乘积测度和著名的Fubini定理以及广义解析函数理论。

In chapter 2 , we shall give an exact introduction to Fourier series which occurred in analysis , multiplicative measure and Fubini theorem in measure theory and some details for the theory of the generalized analytic function .

测度论，特别是量子测度论是量子理论的重要研究课题，我们给出了σ-代数的一个表示定理，并在一类效应代数上改进了著名的Brooks-Jewett收敛定理。

Measurement theory , especially quantum measurement theory , is important subject of quantum theory . We give a representation theory of a-algebra , and improve the Brooks-Jewett theory on effect algebra .

在局部紧空间上的测度论中，正则性是一个比较重要的概念。

Generalization of the Arrow-Barankin-Blackwell theorem in a locally convex space ;

绝对连续是经典测度论中一个极为重要的概念。

Absolute continuity is an important concept in classical measure .

测度论中的代数方法

The Algebraic Methods for Measure Theory

借助这个引理，我们给出了某些混合（拓扑混合或者测度论意义下的混合）的系统中存在着混沌行为的某种新特征，它较之于序列分布混沌更为严酷。

Using the lemma we give a chaotic form more rigorous than distribution chaos in a sequence .

1933年以后，主要以测度论来研究概率论，可以称为测度概率论，这时概率论已经实现了公理化。

Based on the axiomation , the theory of probability has achieved a series of breakthroughs in theories .

应用测度论的知识，给出了非独立随机变量可测函数的期望积分的转换定理的一个证明。

The proof of non independent variable function expected integral transference theorem is given by measure theory in this paper .

在本系列论文中，研究了相应于多重线性映射的强测度论；

In this series of papers , a theory of the strong measure related to a multilinear mapping is studied ;

利用测度论工具对随机过程进行深入的研究时，往往需要假设随机过程具有某种可测性。

For deepgoing study of stochastic processes by measure theory , a hypothesis that stochastic processes possess some measurability is often required .

从测度论观点，给出了模糊集合的另一种描述及模糊测度运算。

From the point of view of measure theory , this paper presents a new description of fuzzy sets and their measure-based operation .

主题包括测度论，极限定理，包围概率和期望，耦合和斯坦的方法，鞅，马尔可夫链，更新理论，和布朗运动。

Topics include measure theory , limit theorems , bounding probabilities and expectations , coupling and Stein 's method , martingales , Markov chains , renewal theory , and Brownian motion .

本文介绍了如何用超限归纳法来作出σ环的构造，以便证明测度论中的某些定理。

This piece describes how to work out the structure of the o-ring by using the transfinite induction , so that it is easier to prove some of the principles in the measure theory .

本文以测度论为基础，在严谨的数学理论基础上，建立了一个由离散型随机变量和一个多维连续型随机变量构成的一种新型的理论分布模型&多维复合极值分布模型。

Based on the measure theory and religious mathematics theory , a multivariate compound extreme distribution model is developed in this dissertation , which is composed of discrete random variable and a multivariate continuous random variable .

基于测度论的方法可导出异方差混合转移分布模型的一阶、二阶平稳条件，为进一步研究该模型的谱奠定了理论基础。

The first order and the second order stationarity conditions of HMTD model can be derived on the bases of measure theory , which will establish the base of theory for deep investigation of spectrum of the model .

在去掉可加性的条件下，将经典测度论中的某些概念加以推广，得到相应的结果.对向量空间的子空间的和的概念不能推广到无限多个子空间的情形进行了讨论。

Some concepts for classical ( signed ) measure are generalized without additivity , and the corresponding results are made . We have discussed sum for subspace of vector space , and cannot popularize sum of subspace to infinitude .

可信性理论是2004年基础数学领域完成的数学分支，它给出了基于测度论的模糊论的公理化体系，并提供了随机性与模糊性综合评估的严格数学基础。

Till 2004 the credibility theory is completed as one of the mathematic branches in mathematic field to give the axiomatic foundation of fuzzy theory based on measure theory , and provide the rigorous mathematic foundation of probability and fuzziness evaluations .

然后利用鞅测度和概率论理论讨论了离散时间的上升敲出期权的二项式定价模型，并推导出其定价公式，此公式推广了标准的二项式定价公式；

By means of martingale method and the theory of probability , the binomial pricing model of discrete up-and-out calls is studied and the formula is deduced , which extends the binomial pricing model of the European option .

切测度作为当代几何测度论之最为重要的技术工具之一，其在奇异积分与rectifiability之关系的研究中起重要的作用。

Tangent measures have become one of the most important technical tools in contemporary geometric measure theory and have played a major part in the study of the connection between singular integrals and rectifiability .

模糊测度的扩张是模糊测度论中一个非常重要和难度较大的课题。

The Extension of fuzzy measures is a very important and rather difficult problem in fuzzy measure theory .

模糊测度与模糊积分理论是经典测度论的延伸，而模糊测度空间中可测函数列与模糊积分的收敛问题始终是一个比较核心的问题。

Fuzzy measure and fuzzy integral theory is an extension of the classical measure theory , the convergence problem of measurable function sequence in fuzzy measure space and fuzzy integral is always a core problem .

通过引入计数测度，将数学分析中的无穷级数与测度论里的抽象积分联系起来，并且在此基础上对无穷级数的一个定理给出了较为简洁的证明。

This paper connects the infinite series in mathematical analysis with the abstract integral in measuring theory through introducing the counting measuring and on the basis of it , the author gives a more compact proof to a theorem on infinite series .

在正则测度生成的过程中，有关容度和测度的关系是经典测度论中的一个比较重要的命题。

In the induction of Borel measure , we always discuss the relative between content and measure .