抽象函数的Riemann积分  

Riemann Integral of Abstract Functions

作　　者：李君[1] 

机构地区：[1]天津科技大学理学院,天津300457

出　　处：《天津科技大学学报》2008年第1期80-82,共3页Journal of Tianjin University of Science & Technology

基　　金：天津科技大学科学研究基金资助项目(20070205)

摘　　要：令是定义在[a,b]上,取值于实Banach空间X的抽象函数,给出了的弱Riemann积分的等价叙述.同时,讨论了l p(1<p<+∞)上取值的抽象函数的弱Riemann积分与Riemann积分的关系.目前广泛应用的Pettis积分是Riemann积分的一种推广,举了一个反例说明弱Pettis可积的抽象函数不一定Pettis可积.Let φ be an abstract function on [a,b] and has values on Real Banach space X , the equivalent description was given on the weak Riemann integral of φ, at the same time, the relations between the weak Riemann integral and the Riemann integral in lp （1 〈 p 〈 ＋∞） was discussed. As a kind of popularized form of the Riemann integral, Pettis integral is extensively applied.We give an example to prove that an abstract function may not be Pettis integral function though it is weak Pettis integral function.

关 键 词：抽象函数 RIEMANN积分 弱Riemann积分 PETTIS积分 

分 类 号：O177.3[理学—数学]