在数学中，以数学家格奥尔格·康托尔命名的康托尔函数，是一个一致连续，却不绝对连续的函数。

康托尔函数 c : [0,1] → [0,1] ，对于x∈[0,1]，其函数值c(x)可由以下步骤得到：

例如：

In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is also referred to as the Cantor ternary function, the Lebesgue function, Lebesgue's singular function, the Cantor-Vitali function, the Devil's staircase, the Cantor staircase function, and the Cantor-Lebesgue function. GeorgCantor (1884) introduced the Cantor function and mentioned that Scheeffer pointed out that it was a counterexample to an extension of the fundamental theorem of calculus claimed by Harnack. The Cantor function was discussed and popularized by Scheeffer (1884), Lebesgue (1904) and Vitali (1905).