黎曼积分

几何体Ω上黎曼积分的统一定义与性质

The Unified Definition and Property of Riemann Integral on Geometrical Figure Ω

黎曼积分与多值函数的极限

Riemann Integral and Many-Valued Function

本文将数学分析中R积分（即黎曼积分）的区间可加性加以推广，给出了R积分区间可列可加性。

In this paper , we generalize the finite additivity of integral interval in mathematical analysis and give the countable additivity of integral interval .

实变函数中有几个克服了黎曼积分的缺陷的积分极限定理：控制收敛定理、Levi引理、Fatou引理。

Real variable function theory is composed of three integral limitation theorems including Control Convergence theorem , Levi Lemma , Fatou Lemma .

基于黎曼积分的同分布原理及应用

Same Distribution Principle Based on Riemann-Integral and its Some Applications

关于广义非正常黎曼积分的注记

On Generalized Non - ordinary Riemann Integrals

本文首先研究形如的二型模糊值黎曼积分。讨论此种类型模糊值积分的近似计算问题。

In this thesis , first we discuss the computations of fuzzy Riemann integral of the form .

而由于黎曼积分具有局限性，黎曼积分只能用于连续函数类的积分。

And because of the limitations of Riemann Integration , it can only be used for continuous function .

本文试图用多值函数的极限说明黎曼积分的定义。

In this paper the definition of Riemann integral haus been given by using the limit of many-valued function .

关于黎曼积分定义教学的新探索牛顿积分与黎曼积分之异同

Teaching of Mathematics Short but Reasonable Reasoning for the Riemann Integral Similarities and Differences between Newton Integral and Riemann Integral

用积分和的极限定义的黎曼积分对于初学者来说是一个很难理解的概念。

It is difficult for learner to understand the concept of Riemann integral which is defined by using the limit of Riemann sum .

文章利用达布和理论，讨论了黎曼积分的可积性问题，给出了一个可积的充分必要条件。

Based on Darboux theory , this paper discussed the integrability of the Riemann Integral and provides a necessary and sufficient condition for integrability .

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 .

分析了诸多积分概念的共性，抽象出黎曼积分的定义，给出了黎曼可积的条件。

This paper sums up the common character of the concept of many integrals , abstracts the concept of Riemann integral and gives the integral conditions of the Riemann integral .

关于黎曼&斯蒂吉司积分的乘积型求积公式

On Product Type Quadrature Formulas of Riemann-Stieltjes Integrals

黎曼可积函数序列的极限函数为黎曼可积的充要条件&黎曼积分号下取极限的充要条件

A Necessary and Sufficient Condition for Riemannian Integrability of the Limit Funtion of a Sequence of Riemann Integrable Functions Exchange Order between Integration Computation and Limit Computation