闭区间上连续函数性质的推广

Generalization of Properties of Continuous Functions in the Closed Interval

在闭区间连续函数的性质的基础上,把闭区间推广到开区间及无限区间,进一步把区间推广到可测集,把连续函数推广到可测函数,得到了几个不同形式的闭区间连续函数性质的推广,使闭区间连续函数的性质得到了丰富.

In this paper,based on the properties of continuous functions in closed intervals,we generalize closed intervals to open intervals and infinite intervals,then measurable sets,and then continuous functions to measurable functions.Several different forms of continuous functions in closed intervals are obtained,which enriches the properties of continuous functions in closed intervals.