关于叶果洛夫定理和Lebesgue定理的扩展  

Expansion about EropoB and Lebesgue

作　　者：阎旭[1] 

机构地区：[1]山东师范大学数学科学院,济南250014

出　　处：《科学技术与工程》2008年第17期4953-4955,共3页Science Technology and Engineering

摘　　要：叶果洛夫定理和Lebesgue定理中共有的条件"fm(m=1,2,…)是E上几乎处处有限的可测函数"可以减弱为"fm(m=1,2,…)是E上的可测函数";"f有限a.e于E"可减弱为"f有限a.e于E或f无限a.e于E"。给出在这种条件减弱的情况下三种收敛的关系。The strength of hypothesis in both EropoB Theorem and Lebesgue Theorem-＂ The function fro （m = 1, 2… ） which is finite almost everywhere on E（ abbreviated to fm is finite a. e on E）is measurable. ＂-can be weakened as ＂fm （ m = 1,2…） is a measurable function on E＂ ; The strength of the hypothesis＂f is finite a. e on E＂ can be weakened as＂ f is finite a. e on E orf is infinite a. e on E＂. Under this condition that the strength of the hypothesis is weakened, the relationships are analyzed among these three kinds of convergence.

关 键 词：几乎处处收敛 近一致收敛 依侧度收敛 

分 类 号：O174.1[理学—数学]