有限测度

It was conjectured in [31] that: if Ms ∈ L~1 for any measurable set E of finite measure,then f ∈ L~n.

在文献[31]中他们猜测：如果对任意有限测度集E，M_S∈L~1，那么f∈L~n。

In Chapter 4we make more study about the properties of the multifractal Hausdorff mea-sure.The existence of finite measure subsets and the Frostman theorem areproved in this chapter.

第四章我们进一步讨论重分形Hausdorff测度的性质，证明了关于重分形Hausdorff测度的有限测度子集的存在性及Frostman定理。

It is well-known that for f with compact support in [66] Stein proved that: M G ∈~L~1 for any measurable set E of finite measure if and only if f ∈ L ln~+ L.

当f有紧支集时，关于它的极大函数的可积性Stein在[66]有个著名的结果：对任意有限测度集E，M∈L~1当且仅当f∈Lln~+L。

Dorea advanced kernel estimation p of p ,which is a general density with respect to a σ-finite measure v on.ξ is a σ-field of subsets of ER. Some qualities have been gotten. And it has been proved that those results consist of theories of classical kernel estimation for continual density and further extended theories of disperse kernel estimation.

Y Dorea在2001年提出了关于上的σ-有限测度v的一般密度函数P的核估计几，其中ER，ξ是E的一个σ-域，得到了一些结果，并且验证了所得结论包含经典的连续密度核估计的结论，还进一步延伸了离散分布核估计的结论。

In [1] and [35] Bagby and Gomez independently proved that there are many functions f ∈ L ln~+ L(R~2) such that M_s ∈ L~1 for any measurable set E of finite measure.

在[1]和[35]中他们分别证明了存在许多函数f∈Lln~+L(R~2)使得对任意有限测度集E，M_S∈L~1。

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。

Because M_S ≤ M~*, if f G L~n, then M_S ∈ L~1 for any measurable set E of finite measure.

因为M_S≤M~*，所以当f∈L~n时对任意有限测度集E，M_S∈L~1。

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。

Firstly,different control strategies for sensor management are modeled by the real language measure. The legal behavior of control strategy modeled by FSA can generate a partially ordered set of controlled languages. Then an identification method of the language measure parameters based on an FSA model is proposed. The language measure creates a total ordering on the performance of the controlled languages.

首先，建立传感器管理控制策略的有限状态自动机模型，通过对可控制事件的非使能设定，描述不同控制策略；提出语言测度参数的递归估计方法与停止规则，并根据有限状态自动机模型产生语言的测度获得各种传感器控制策略的性能指标。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。