Henstock积分Newton-Leibniz公式的简捷证明  

Simple Proof of Newton-Leibniz Formula of Henstock Integral

作　　者：李伟[1] 宋述刚[2] 

机构地区：[1]集美大学理学院,福建厦门361021 [2]长江大学信息与数学学院,湖北荆州434023

出　　处：《长江大学学报（自然科学版）》2017年第1期40-43,共4页Journal of Yangtze University(Natural Science Edition)

基　　金：福建省自然科学基金项目(2015J01585)

摘　　要：Newton-Leibniz公式是微积分学基本定理的一个重要应用,其建立了定积分与被积函数的原函数之间的联系,使得计算定积分问题从求和式的极限转化为求被积函数的原函数值差的问题。在Riemann积分、Lebesgue积分、Newton积分和δ(x)精细分划的基础上,建立了Henstock积分有关的基本概念,简述了Henstock引理及其证明,由此给出Henstock积分中的Newton-Leibniz公式,并给予简捷证明。Newton-Leibniz formula is an important application in basic theorem of calculus,it establishes the connection between the definite integral and the integrand function,thereby the problem of the definite integral calculation is transformed from the limit of sum to the function of value.In this paper,on the basis of fine division of Riemann Integral,Lebesgue Integral,Newton Integral andδ(x),the related basic concepts of Henstock Integral is established,the relevant definition of Henstock Integral is sketched and proven,from which the Newton-Leibniz formula in Henstock Integral is given,and a simple proof is also given.

关 键 词：RIEMANN积分 δ(x)精细分划 HENSTOCK积分 连续函数 

分 类 号：O171.2[理学—数学]