Cantor函数的曲线弧长

Arc Length of the Cantor Function

通过分析特殊的Cantor函数的取值特点,讨论了Cantor函数曲线及推广的Cantor函数曲线的可求长问题,并且得到一个新的判断曲线可求长的方法,从而证明了Cantor函数曲线及推广的Cantor函数曲线可求长.并采用逼近的方法得到Cantor函数曲线及推广的Cantor函数曲线的弧长.

By analyzing the behavior of the Cantor function at some special points,we discuss the measurability of the Cantor function and the extended Cantor function respectively,and obtain a new criterion of the curve measurability.As a consequence,we show that both the Cantor function and the extended Cantor function are measurable.Based on the approximation method,we find that the arc length of the Cantor function or the extended Cantor function.