测度

In the third chapter,we will discuss the properties of Haar measure,and then wewill prove the Ergodic theorem;at last,we follow Dale,Baaj and Skandalis to give twoexistence theorems of Haar measure,which we proved in different language.

在第三章我们讨论了Haar测度的性质，证明了〓双代数中的平均遍历定理，并且用算子的观点叙述证明了Dale和Baaj、Skandalis分别给出的两个Haar测度存在定理。

After introducing some basic results from ergodic theory, two probIems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation. They correspond to the functional analysis and numerical analysis of the Frobenius-Perron operator associated with the dynamical system.

首先介绍了遍历理论的一些经典结果；然后着重研究了对应于混沌映射的绝对连续不变测度的存在性与计算问题，这归结于相应的Frobenius-Perron算子的泛函分析与数值分析；最后《确定性系统的统计性质》介绍了Shannon熵、Kolmogorov熵、拓扑熵以及Boltzmann熵，并给出了不变测度的一些最新应用。

Jiu Ding,Aihui Zhou,Statistical Properties of Deterministic Systems Statistical Properties of Deterministic Systems discusses the fundamental theory and computational methods of the statistical properties of deterministic discrete dynamical systems. After introducing some basic results from ergodic theory, two probIems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation.

摘要本书介绍的是确定性离散动力系统统计性质的基本理论与计算方法，首先介绍了遍历理论的一些经典结果；然后着重研究了对应于混沌映射的绝对连续不变测度的存在性与计算问题，这归结于相应的Frobenius—Perron算子的泛函分析与数值分析；最后本书介绍了Shannon熵、Kolmogorov熵、拓扑熵以及Boltzmann熵，并给出了不变测度的一些最新应用。

To enhance the qualitative measurement for regional sustainable development has an explicit function of facilitating the environmental construction of the ecosystem.

加强对区域可持续发展水平的定量测度，对促进生态环境建设起着明显的推动作用。为此，用"和度"与"合度"作为区域可持续发展水平的测度指标，测量了1992、1995、2000年全国各省市区生态资产的总量及单位面积上的生态资产密度，并据此分析了各省市区国内生产总值变化与其生态资产间的关系。

By studying measure theory, the students are asked to understand σ-algebras, measure, measurable functions, integral, the measure theory of product spaces, Fubini theorem, and the representation theory of Boolean algebras.

通过本课程学习，使学生掌握σ-代数、测度、可测函数、积分，初步掌握乘积测度空间的构造及Fubini定理，以及布尔代数的表示理论。

A tetrahedral mesh with up to somehundred thousands nodes can be generated within hours with a personal computer.. By using the general harmonic mean of heat conduction coefficient, a new discretization method in the unstructured grid with anisotropic and heterogeneous media is developed.

生成的网格可以按照给定的纵横比实现剖分（纵横比可高达2000），这样就克服了非结构网格难于在粘性支层内使用的缺点；给出了切平面测度和主曲率测度矩阵的建立方法，结合各向异性网格生成技术，实现了三维空间曲面剖分，为三维实体剖分做了准备。

The Hausdorff measure is the most important one among above three measures.

Hausdorff测度是上述三种测度中最为重要的一个。

The exact Hausdorff-type measures of its image set and graph set are provided and it is proved that the usual Hausdorff measure functions for its image set and graph set are still correct measure functions.

在一定条件下，通过一些更小的测度函数给出了象集和图集的有限正的Hausdorff型测度。

The concepts of Hausdorff dimension and measure have been introduced for near one hundred years. There are lots of works have been done on the calculation and estimation of Hausdorff dimension, such as the result of self-similar set which satisfies open set condition.

Hausdorff维数与测度的概念被引入至今己近百年，Hausdorff维数计算与估计的研究己取得相当进展，如关于满足开集条件的自相似集的结果，但对Hausdorff测度的计算而言所得的结果却不多。

Firstly,the classification of probability rule is analyzed on the base of classic rough set concepts and extended to the equal relation of set in the indefinite system,namely,the upper and lower approximation space of research set is expressed in the form of conditional probability;then,according to the measure of probability rule,the attributes reduction is carried out and the classification rule is extracted by using the related parameters of condition attributes' impend precision from the angle of conditional probability;Finally,the related simulation test result is given and the result shows the classification rules with probability measures is more rational.

首先在经典粗糙集概念的基础上分析概率规则的分类，并将其推广到不确定系统的集合等价关系中，即用条件概率的形式表示研究集合的上下近似空间；然后根据概率规则的测度从条件概率的角度利用条件属性的逼近精度的相关参数进行属性集的约简进而提取分类规则；最后给出了相关的仿真实验结果，结果表明带有概率测度的分类规则更合理。

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。