连续函数列的极限函数需要满足的充分条件和必要条件  

Sufficient Condition and Necessary Condition for the Limiting Function of a Sequence of Continuous Functions

作　　者：郑利凯[1] 

机构地区：[1]内蒙古民族大学数学学院,内蒙古通辽028000

出　　处：《河北北方学院学报（自然科学版）》2011年第2期1-3,7,共4页Journal of Hebei North University:Natural Science Edition

基　　金：内蒙古自治区自然基金资助项目(2010MS0119)

摘　　要：研究Rn上的函数f是Rn上一列连续函数{fn}的极限函数的必要条件和充分条件.利用Baire定理,给出了连续函数列的极限函数必须满足的必要条件.通过构造连续函数列逼近已知函数,给出了连续函数列的极限函数必须满足的充分条件.The paper studies the necessary condition and sufficient condition for function f on Rn being the limiting function of a sequence of continuous functions {fn}.On the basis of Baire theory,a necessary condition for a function on Rn being the limiting function of a sequence of continuous functions has been found.By constructing a sequence of continuous functions to approximate a known function,the paper gives a sufficient condition for a function on Rn being the limiting function of a sequence of continuous functions.

关 键 词：极限函数 连续函数 Rn 必要条件 充分条件 Baire定理 

分 类 号：O174.11[理学—数学]