测度

Keywords: multi-parameter stochastic process; Hausdorff measure; fractal sets; multifractal analysis; sample path

中文关键词：多指标随机过程； Hausdorff测度；分形集；重分形分析；样本轨道

In Chapter One,we find the relationship between strong open set condition , Hausdorff dimension,the positivity of the Hausdorff measure and β space of graph-directed self-similar sets in complete metric spaces.

在第一章中，我们讨论了在度量空间中，图定向自相似集的强开集条件、Hausdorff维数，正的Hausdorff测度和β空间之间的关系。

The paper developed similarity measure of real number vague sets based on score function to i-v Vague sets by using the mean of interval number and Hausdorff metric respectively, and compare the advantage and disadvantage of different methods.

分别利用区间的中值和Hausdorff测度将基于记分函数的实数型Vague集的相似度方法扩展到i-vVague集上，比较各种方法的优缺点。

On one hand, the result of evaluation can help enterprise understand oneself foundation in resources allocation.

企业信息资源配置过程中评价与测度也是其中重要的一环。

A divisive hierarchical clustering algorithm for blind classification of radar emitters based on grey relational measure is proposed.

提出了一种基于灰关联测度的分裂式层次聚类算法来实现雷达辐射源信号的盲分类。

Paul Erds once posed the following problem about real line R: is it true that, for every infinite set X, there is a closed set E with positive lebesgue measure such that E doesn't contain any subset similar to X (I.e., there is no subset of E, which is a linear homeomorphic image of X). In 1984, K. J. Falconer proved the following: for a decreasing sequence of positive numbers {xn} such that \%lim\%xn=0 and \%lim\%(xn+1)/=1, Erds problem has a partial positive answer.

叶盛 Paul Erds曾提出如下关于实直线R的问题：是否对R的每一个无限子集X，都存在一个具有正测度的闭子集E，使得E的任何子集都不相似于X(E的任何子集都不与X线性同胚)。1984年，Falconer证明了如下结论：对于一个满足limxn=0和lim(xn+1)/=1的单调递减的正实数列{x n}，Erds问题有一个部分肯定的解答。

The method used to check for completeness is based on a set of sufficient conditions proposed by Guttag and Horning We weakened the definition of the measure function and the conditions under which an extension function can be converted to constructors and generators.

完备性的验证方法是，以Guttag-Horning的一组完备性充分条件为基础，放宽其中测度函数的定义，以及扩充函数可以转为生成函数与构造函数的判别条件，拓广了充分条件的适用范围。

Just as God's mind is unfathomable, so there are illimitable depths in ????ure:"the stores of truth laid up in it are inexhaustible."

正如上帝的心意是无法测度的，同样地，《圣经》里有无限的深渊，「它《圣经》所储藏的珍宝是使用不尽的。

Meanwhile, there are academic dilemmas for social capital in fuzzy definition and immeasurability. The unbalanced distribution may lead to resources monopoly and market segmentation, and the lack of universal trust may go against economic development.

同时，社会资本也存在定义模糊和难以测度的理论困境，其非均衡分布还可能造成资源垄断和市场分割，而缺乏普遍性的信任还会阻碍经济的发展。

The mind can never be great, for what is great is immeasurable.

头脑永远不可能是伟大的，因为伟大的是不可测度的。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。