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

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.