Sufficient Condition and Necessary Condition for the Limiting Function of a Sequence of Continuous Functions
Zheng Li-kai · Journal of Hebei North University · 2011
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.