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Their properties and the connection with Lebesgue integral sum and integral are studied.

研究了它们自身的性质及与勒贝格积分和、勒贝格积分的关系。

Here we discuss the limitations of the Riemann integral and the greater scope offered by the Lebesgue integral.

在这一章里我们讨论黎曼积分的限制以及勒贝格积分提供的更大的可能性。

For simplifying and unifying the defini- tions,and for understanding and mastering the concepts of Lebesgue integral from different angle,it is very significant to study how to define Lebesgue integral,and to prove the equivalence of different defin- tions.

关于L积分理论的研究，特别是关于L积分定义的研究，研究新的定义方法以简化L积分的定义，证明各种定义的等价性以统一L积分的定义，引起了国内外专家学者的广泛关注，并进行了许多深人的研究l一6〕。

There are proved the theorems on convergence of sequences of the integral, which are similar to Levi's theorem, Fatou's theorem and so on in Lebesgue's integral.

4中引进了一类特殊的所谓λ次可加模糊测度空间，给出了这种测度空间上收敛性的Егоров定理和Riesz定理并得到了该空间上的模糊积分在积分号下取极限的一些充分条件。

Which introduces kids and their extension to the primary form of the Riemann integral forms can store and then to be accumulated under the Lebesgue integral form and find the links between these three forms of proof and provement.

其中主要介绍不等式的初等形式及其推广到Riemann可积下的积分形式，然后到Lebesgue可积下的积分形式，并寻找这三种形式之间的联系和证明

After introducing the concept of fuzzy measures and Choquet fuzzy integral, information fusion for target recognition can turn into generalized Lebesgue integral of recognition result with respect to the degree of importance of source.

引入模糊测度和 Choquet 模糊积分的概念后，信息融合目标识别可转化为各信源识别结果关于信源重要程度的广义 Lebesgue积分。

Firstly,the article theoretically expounds the superiority of Lebesgue Integral ,then through the detailed cases analyzes its superiority shown in the practical application compared to Riemann Integral.

文章首先从理论上阐明勒贝格积分的优越性，然后通过具体实例详细探讨勒贝格积分相对于黎曼积分，在实际应用中体现出的巨大优越性。

Methods By using Lebesgue integral and Fouries series, area transformation formula of planar domain and variant transformation formula of double integral are discussed.

利用勒贝格积分和傅立叶级数讨论平面区域面积变换公式和二重积分变量变换公式。

With the help of the concepts of Lebesgue measure and Lebesgue integral in real function,the mathematics model of concurrent design of life-oriented progressive die is advanced. Which were the Lebesgue measure and Lebesgue integral of die substructures and a general mathematics model of the relation between progressive die structure and die substructures.

运用实变函数中的Lebesgue测度和Lebesgue积分的概念，结合面向寿命的级进冲模并行设计的特点，建立了面向寿命的级进冲模并行设计数学模型—模具子结构的Lebesgue测度和Lebesgue积分，提出了级进冲模结构与模具子结构关系的一般数学表达式。

After constrcting the perfective space , prove that this space is just the space of lebesgue integratiable function , thus explain that lebesgue integral is the form of the perfective riemann integral

在构造了完备化空间之后，证明了该空间就是勒贝格可积函数空间，从而说明了黎曼积分的完备化形式是勒贝格积分。

A carrier gas such as nitrogen is directed through line 20 and valve 22 to connect with line 26 and mix with the gas sample.

如氮气之类的载体通过管线20和阀22引入，与管线26相通，与气体样品混合。

But for the most part, knaves and parasites had the command of his fortune

然而支配他的家产的大多是恶棍和寄生虫。