测度

First, we discuss several theories of risk measures respectively such as theories ofcoherent measures of risk, spectral measures of risk and distortion measures of risk.Within the framework of these theories, we discuss and compare standard deviation,mean absolute deviation, lower partial moment, Ginis difference, VaR, CVaR and soon. We conclude that CVaR is superior to other measures with respect to theoreticalproperties.

首先，本文分别讨论了一致风险测度理论、谱风险测度理论、失真风险测度理论和随机占优一致风险测度理论等风险度量评价理论，在这些理论框架内讨论和比较了标准差、平均绝对离差、下偏位矩、基尼均差、VaR以及CVaR等风险度量。

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。

By discussing the position hypothesis of fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying the measure calculation equations, the measure of self-similar fractals which include middle-third Cantor set, Koch curve, Sierpinski gasket and orthogonal cross star are calculated and analyzed.

通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设，进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式，给出分维导数与分数阶导数的区别，随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式，给出了其与目前 Hausdorff 测度方法的区别，并对包括三分 Cantor 集合、 Koch 曲线、 Sierpinski 垫片及正交十字星形等自相似分形在内的测度进行了计算分析。

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 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。

The measures concerned in this paper including Hausdorff measure, packing measure and Hausdorff centred measure.

所涉及到的测度有Hausdorff测度，填充测度与Hausdorff中心测度。

With four continuity of non-additive set function and the relation of four convergences of the measurable function sequence,four forms Lebesgue theorem about measurable closed-valued functions on monotone measure space are discussed,respectively.

在经典测度论中，Lebesgue定理刻画了实值可测函数序列几乎处处收敛和依测度收敛之间的关系。1984~1986年，王震源[9]先后提出了较弱的"自连续"、"零可加"、"伪自连续"、"伪零可加"等重要概念，讨论了模糊测度空间上单值可测函数序列各种收敛之间的关系，推广了经典测度论中著名的Lebesgue定理以及其他定理。

Lebesgue measure is introduced in knowledge base, knowledge measure and knowledge measurable sets are defined.

在知识库中引入勒贝格测度，定义了知识测度和知识可测，对比勒贝格测度研究了知识测度的性质，并得出了波雷耳集与知识可测集等价等强于勒贝格测度的性质。

If 〓 is an absolutely continuousmeasure and is represented by a measurable function f on Q,then u is said tobe the generalized solution of(1),and 〓 to be the parabolic Monge-Amperemeasure.

定义1由legendre变换定义了一个Q上的测度〓（4）其中〓为〓空间中的Lebesgue测度，若〓是一个绝对连续测度且在Q上由可测函数〓表示，则称u为方程（1）的广义解、称测度〓为抛物型Monge-Ampère测度。

The majority of the literatures about the measurement of knowledge management favors to the performance evaluation, however there are many disadvantages about the performance evaluation of knowledge management. Therefore this paper choses the level evaluation of knowledge management instead of the performance evaluation as the research direction.

但是分析已有的知识管理测度方面的文献，发现大部分研究偏重于知识管理的绩效测度，然而绩效测度并不是知识管理的全部直接成果，具有滞后性，不利于企业的日常管理，所以本文在绩效测度和水平测度之间选择了知识管理的水平测度作为研究的方向。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。