勒贝格积分相对于黎曼积分的优越性  

Advantage of Lebesgue over Riemann integral

作　　者：刘晓辉[1] 刘文菡[2] 

机构地区：[1]河北工程大学理学院,河北邯郸056038 [2]邯郸师院数学系,河北邯郸056005

出　　处：《新余高专学报》2006年第3期92-93,共2页Journal of XinYu College

摘　　要：对勒贝格积分进行了深入研究,重点从三方面详细论述了勒贝格积分相对于黎曼积分的优越性,首先勒贝格可积函数的范围比黎曼积分广泛,其次在勒贝格积分意义下,积分与极限交换顺序的条件比较弱,最后从微积分基本定理的应用范围上再次加以证明。The authors made further research into Lebesgue integral, mainly dwelling on the advantages of Lebesgue integral over Riemann integral from three aspects. First, the scope of Lebesgue integral is wider than Riemann integral; Second, in a sense of Lebesgue integral, the condition of exchange order of integral limit is very weak; at last, the application scope of the basic differential integral theorem proves the result.

关 键 词：勒贝格积分 黎曼积分 优越性 极限 范围 

分 类 号：O174[理学—数学]