G可积函数的Lebesgue可测性  

The Lebesgue Measurability of the G Integrable Function

作　　者：李毅侠[1] 董新汉[2] 王体福[2] 

机构地区：[1]湘南学院数学系,郴州423000 [2]湖南师范大学数学与计算机科学学院,长沙410081

出　　处：《应用数学学报》2007年第2期327-333,共7页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10571049);湖南省自然科学基金(05JJ30011)资助项目.

摘　　要：Botsko在连续和可导的知识基础上推广了Riemann积分,得到了一种新的积分,称为G积分．G积分既不同于Riemann积分也不同于Lebesgue积分．本文通过对G积分的研究,得到了G可积函数一定Lebesgue可测,从而有界G可积函数一定Lebesgue可积;同时我们还证明了这两个积分值相等．On the basis of the concepts of continuity and the derivative, Botsko generalized the Riemann integral and obtained a new type integral which is called the G integral. The G integral is different from the Riemann integral and the Lebesgue integral. In this paper, we study the G integral and obtain that a G integrable function is Lebesgue measurable, then a bounded G integrable function is Lebesgue integrable; also we prove that these integrals are equal.

关 键 词：G可积 Lebesgue可测 LEBESGUE可积 

分 类 号：O172.2[理学—数学] O174.1[理学—基础数学]