查询词典 measure space

Based on the theory, the differential geometry of statistical model proposed by Amari is generalized from probability space to Sugeno measure space, and a new notion of fuzzy manifold based on Sugeno measure is proposed, including the fundamental differential-geometrical structures of statistical models, the tangent space, and the Riemannian metric in a fuzzy manifold.

第四章介绍了Sugeno测度空间上随机变量的数字特征，在此基础上将学者Amari提出的统计流形从概率测度空间推广到Sugeno测度空间，提出了一种基于Sugeno测度的模糊流形分析方法，包括Sugeno模糊模型的基本微分几何结构，模糊流形中的切空间、黎曼度量。

In the fourth chapter,first of all,a metric space is derived by the Loeb measure space which is a standard measure space,follow that the Completeness,separability and the Baire theorem are expressed.

第四章中，首先由Loeb测度这个标准测度空间导出度量空间，接着讨论了该度量空间的完备性和可分性以及其Baire定理(来源：A8525B52C论文网www.abclunwen.com)。

First, the partial derivative is defined, based on the convergence in probability measure in the probability measure space.

本文首先在概率测度空间上，利用依概率测度收敛，定义了多随机变量函数的偏导数，并且偏导数的计算式可以通过替换实值函数的对应的偏导数中所有的实变量替换为随机变量得到。

The effective prediction space concept is established, On the base of these, this paper deduces two representations' evaluating equation, one evaluates the prediction error and the other evaluates the prediction error in limited space. First, the error transfer characteristic among subsystems at different space locations is analyzed, and the direct transfer characteristic from discrete standard measure space to the workpiece measure space under measured in measure system is proven. Second, the error reconstruction condition and method of mapping from discrete standard measurement system to continuous standard measurespace are analyzed.

分析了不同空间位置子系统间的误差传递特性，证明了在测量系统中离散标准量值空间向被测量工件量值空间的直接传递性；分析了离散标准量系统向连续量值空间映射的误差重构条件和方法；基于测量样本的有限距离的平稳性，证明了预报模型对动态测量误差的有限收敛性和预报误差的可测度性，进而证明了以离散标准量值系统对被测工件预报修正的可行性和合理性。

In the second part, we give the definition of Loeb measure space ofσ- finite measure space, discuss its properties; Then the Loeb measure space of image measure has been constructed; Finally, the definition of Loeb counting measure is given, by which, a construction of Lebesgue measure has been given, and discuss some simple properties of Lebesgue measurable and integrable function.

在第二部分里，首先给出σ-有限测度空间的Loeb测度空间的定义，讨论该空间上的一些简单性质；接着讨论了像测度的Loeb测度的构造及其性质；随后定义了L(来源：A14BC论文网www.abclunwen.com)oeb计数测度，并用Loeb计数测度给出Lebesgue测度的一种构造形式，同时讨论了Lebesgue可测和可积函数的一些简单性质。

In the fifth chapter,we mainly discuss the relationship of the metric space induced by a Loeb measure space and the metric space induced by a internal finitely additive measure space.

在第五章，我们重点讨论了由有限测度空间导出的度量空间和由内有限可加测度空间导出的度量空间的关系，然后在此关系的基础上研究了由内有限可加测度空间导出的度量空间的性质。

In this paper,the nonstandard analysis theory is used for inducing a metric space by a Loeb measure space.On this basis,a metric space is induced by a internal finitely additive measure space.The close relationship between the metric space induced by a Loeb measure space and the metric space induced by a internal finitely additive measure space is illustrated with the concepts and some properties of Loeb measure.Then,some properties of the metric space that induced by a internal finitely additive measure space are studied.In the first two chapters,we first Succinctly present the origin,development and research states of the nonstandard analysis.Then,the theoretical foundation of nonstandard analysis as well as the axiomatic nonstandard analysis are given.Finally, the nonstandard model and the saturation model are discussed,as well as some natures of the nonstandard model and several equivalent conditions of saturation model are given.

本文利用非标准分析理论，在由Loeb测度空间导出度量空间的基础上，由内有限可加测度空间导出了度量空间，并借助Loeb测度的概念和若干性质证明了由标准的测度空间导出的度量空问和由内有限可加测度这个非标准的测度空间导出的度量空间有着密切的关系，在此关系的基础上还研究了由有限可加测度这个非标准的测度空间导出的度量空间的性质在第一、第二章里，我们首先简单介绍了非标准分析的产生、发展及研究现状，接着给出了非标准分析的理论基础以及公理化的非标准分析，进而讨论了非标准模型和饱和模型，并给出了非标准模型的一些性质和饱和模型的若干等价条件。

In this paper, many concepts and propositions in measure theory are described and characterized by nonstandard analysis in nonstandard saturation model, and some important conclusions in Loeb measure space are extended and developed to a certain extent.

本文在非标准饱和模型下，利用Loeb测度对测度论中的若干概念和命题进行了非标准描述和刻画，并在一定程度上推广和发展了Loeb空间的一些重要结论。

The relations among three kinds of structural characteristics of fuzzy measure:(1) pseudometric generating property;(2) pseudometric generating property of type p;(3) null-null additivity,and the convergence for sequence of measurable function on semi-continuous fuzzy measure space are discussed.

李军讨论了下半连续模糊测度的3种结构特性：(1)伪距离生成性质；(2)p类型伪距离生成性质；(3)零-零可加性与半连续模糊测度空间上可测函数序列的收敛性之间的关系。

The measure of measurable space could reflect its measure space.

计算模型是对数据融合功能模型的数学描述。

I am sure after a few weeks of adaptation and familiarization I will have no difficulty in functioning on a daily basis in an English speaking society or in participating fully in graduate studies.

在大学的三年的学习生活不仅给予我自身的充实，更重要的是磨练和培养了我较强的自觉能力和严谨，踏实的作风以及不怕困难的精神，对未来充满了信心！

As the first volcanoes erupted, one of the gases that bellowed out was steam.

在第一批火山喷发时，喷出的气体之一就是水蒸汽。