关于Riemann可积函数的本性  

On Essential Feature of Kiemann-Integrable Functions

作　　者：赵显曾[1] 

机构地区：[1]东南大学数学力学系

出　　处：《东南大学学报（自然科学版）》1995年第6期9-13,共5页Journal of Southeast University：Natural Science Edition

摘　　要：本文引进了函数在一点的本性振幅的概念，在Ｒｉｅｍａｎｎ积分意义下，证明了定理：设有界函数ｆ定义于闭矩形Ｉ，在Ｉ上Ｒｉｅｍａｎｎ可积的充要条件是对任意η大于零，Ｅ＿η是一个零面积集。In this paper,we introduce the concept for essential oscillation of a functions at a point.The following theorem is proved in the manner for Riemann integral.Theorem. Assume a function f is defined and bounded on a closed rectangle I=[a,b]×[c,d].The necessary and sufficient condition for f to be Riemann-integrable on I is that area of Eη={M|M∈I and ω[f,M]≥η} is zero for any η>0.

关 键 词：数学分析 连续性 黎曼积分 黎曼可积函数 

分 类 号：O172.2[理学—数学]