勒贝格积分

勒贝格积分创建的思想方法及意义

The Significance and Thinking Way of the Lebesgue Integral

关于勒贝格积分教学的新探

A Kind of New Teaching Opinion about Lebesgue Integral

勒贝格积分三种定义的等价证明

The Proof Equivalence of the Three Definitions of Lebesgue 's Integral

勒贝格积分中微积分基本定理的推广

Extension of Infinitesimal Analysis Elementary Theorem in Lebesgue Integral

本文对五种勒贝格积分定义的等价性给予证明。

This paper gives the proofs about the equivalence of five Lebesgue integral definitions .

利用本质下确界的概念以及勒贝格积分的特性，将积分总极值方法推广到了有界可测函数上，提出了针对有界可测函数的理论算法，并给出了其最优性条件。

An integral-level set conceptual algorithm is proposed for bounded measurable functions , and an optimality condition is obtained .

截断函数在勒贝格积分中的应用&无界函数积分转化为有界函数积分的数学方法

Application of Interruptive Function in Lebesgue Integrals & The mathematical method of infinite function integrals being transferred into finite function integrale

从而使初学者能深刻地体会勒贝格积分与黎曼积分的区别，并在创新思维的培养方面受到启发。

From this , we can more profoundly read the difference between the Lebesgue 's integral and Riemman 's integral , and get enlightenment in creative thinking .

为了使初学者能很好的掌握勒贝格积分，这里将讨论这三种勒贝格积分定义的特征，并给出它们之间的等价性证明。

In this paper , we will present the equivalence proof of the three definitions of Lebesgue 's integral , and discuss the characteristics of the three definitions .

实变函数教材中给出了三种勒贝格积分的定义，这三种定义在形式上存在着很大的差别。

Generally , there are three definitions of Lebesgue 's integral , but much difference exists in the form of the definitions , which will make troubles for the beginners .