测度空间

In the six chapter, we use the methods of reproducing kernel and Carleson measure charactering the pointwise multipliers on the Hardy space, Bergman space on the polydiscs, we also obtain a necessary condition for a composition operator to be a compact operator, and a addition result on the range of composition operator on the Hardy space.

在第六章中，我们利用再生核与Carl e Son测度刻画了多圆Hardy空间到Bergman空间，以及Bergman空间到Bergman空间的点乘子，得到Hardy空间与Bergman空间上复合算子为紧的一个必要条件，以及在Hardy空间上关于复合算子值域的一个结果。

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。

And the sufficient and necessary conditions of the monotone set function which is continuous of the empty set and the full set are given.

李军[6]引入了强序连续性概念，证明了单调测度空间上实值函数的Lebesgue定理成立的充要条件是单调集函数具有强序连续性。

In the first part, firstly, we introduce the nonstandard analysis theory simply. Using the axioms in nonstandard analysis, the nonstandard model is axiomatic approached, and the existence of nonstandard model and the consistence of axioms in nonstandard analysis are proved by the construction of nonstandard model. Secondly, some properties of nonstandard model are discussed, such as transitivity, Boolean properties, etc. Finally, Loeb measure spaceY,L

在第一部分里，首先对非标准分析理论进行了简单的概述，通过用非标准理论中的公理，给出了非标准模型，进而利用非标准模型的构造，证明了非标准模型的存在性和非标准模型中公理的一致性；其次，讨论了非标准模型的一些简单性质，如传递性，布尔代数运算性质等；最后，在内测度空间Y，

179Banach Algebra Techniques in Operator Theory, Ronald G. Douglas180 A Course on Borel Sets, S.M.

Borel集是集合论和逻辑学的重要概念，本书介绍完备可分的测度空间的Borel子集，内容从基本的集合论概念到描述集合论的公开问题。

Considering the inputs of neural networks as random variables, this thesis aims at extending this definition to the probability measure space.

本文旨在当把神经网络各输入变量看作随机变量时，把这种定义推广到概率测度空间。

The Kolmogorov extension proceeds along the following lines: assuming that a probability measure on the space of all functions exists, then it can be used to specify the joint probability distribution of finite-dimensional random variables .

收益的Kolmogorov延长其内容大致如下：假设概率测度空间上存在的所有功能，那么它可以用来指定联合概率分布的有限维随机变量。

Using the measure property of the original space it shows that the quotient space has its self-similar measure, and the support of the measure is the unique attractor of quotient space.

并且利用原空间的测度性质，提出了在商空间中也具有自相似测度，且自相似测度的支撑集就是商空间的唯一的吸引子。

Fractal dimension structure of the Cosmos are explored, and the mathematical foundation, which include the expressions of fractal dimension differential and calculus, regular space integral solutions of fractal dimension differential equations, the fractal calculus definitions of fractal measure as well as the measure computational equation of self-similar fractal, of fractal dimension calculus and fractal measure are given.

摘 要：探讨了宇宙分维构造的形式，给出了分维微积分及分形测度的数学基础，包括分维导数及分维微积分的表述形式、分维微分方程的规整空间积分解、分形测度的分维微积分定义及自相似分形的测度计算方程。

On the aspect of urban spatial distribution DM: Adopting the conception model of combination of location and attribute, the author brings spatial coordinates, spatial relationship and attribute character into the unitive model of spatial computation, studies city's land suitableness evaluation and the method of spatial clustering in division of urban function districts and brings forward the arithmetic of classification layer. Aiming at land spatial optimization allocation, the author puts forward SGA. In this arithmetic selection, crossover and mutation operator are progressed on the space.

在城市空间分布数据挖掘方面：采用空间—属性一体化概念模型，把空间坐标、空间关系和属性特征纳入到统一的空间计算模型，分别对城市土地适宜性评价和城市功能区划分中的空间聚类方法进行了研究，并提出了一种分类图层的平滑算法；针对城市土地的空间优化配置，提出了一种空间遗传算法，该算法中的选择、交叉、变异算子都是在空间上进行的；对多要素离散空间场之间的相关性测度，定义了一种基于信息熵的规范的相关指数，并给出了计算方法。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了