有界闭区间上连续函数列一致收敛的充要条件  

The Necessary and Sufficient Condition of the Uniform Convergence of Continuous Function Sequence in Bounded Closed Interval

作　　者：傅湧[1] 

机构地区：[1]宜春学院数学与计算机科学学院,江西宜春336000

出　　处：《大学数学》2007年第3期117-120,共4页College Mathematics

基　　金：江西省教育厅教学研究资助课题(200410009);宜春学院精品课程项目

摘　　要：判别函数列一致收敛的方法有函数列一致收敛定义、Cauchy一致收敛准则、limn→∞supx∈D|fn(x)-f(x)|=0及Dini定理,本文由函数列的等度连续性,可得出几个有界闭区间上连续函数列一致收敛的充要条件,推广了Dini定理.Method of discriminate function sequence uniform convergence is definition of function sequence uniform convergence, Cauchy＇s test of uniform convergence, llimn→∞supx∈D｜fn（x）-f（x）｜=0and Dini theorem. In this paper, use equifiontinuous of function sequence obtain the necessary and sufficient condition of the uniform convergence sequence of continuous functions in bounded closed interval, generalize Dini theorem.

关 键 词：等度连续 一致收敛 函数列 有界闭区间 

分 类 号：O172.2[理学—数学]