非绝对积分与绝对积分的关系  

Relationship Between Non-Absolute and Absolute Integral

作　　者：田菊蓉[1] 李岚[1] 闫焱[1] 

机构地区：[1]西安文理学院数学系,陕西西安710065

出　　处：《西安联合大学学报》2004年第2期35-39,共5页

摘　　要：说明了Newton积分与Henstock积分为非绝对积分,Riemann积分与Lebesgue积分为绝对积分.讨论了这几种积分之间的关系,证明了Henstock积分是这几种积分的统一形式,同时证明了R([a,b])是不完备空间,H([a,b])是完备空间.This paper explains that Newton integral and Henstock integral are non-absolute integral, while Riemann integral and Lebesgue integral are absolute integral. Furthermore, this paper discusses about the relationships between them. Finally, it proves that Henstock integral is the unified form of these integrals, and that R ( ) is incomplete space, while H () is complete space.

关 键 词：Newton积分 HENSTOCK积分 Rimaann积分 LEBESGUE积分 完备空间 

分 类 号：O172.2[理学—数学]