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Line 39: The Cantor function is the standard example of a [[singular function]]. The Cantor function is non-decreasing, and so in particular its graph defines a [[rectifiable curve]]. {{harvtxt\|Scheeffer\|1884}} showed that the arc length of its graph is 2. Note that the graph of any nondecreasing function such that <math>f(0)=0</math> and <math>f(1)=1</math> ishas length not greater than 2. In this sense, the Cantor function is extremal. ===Lack of absolute continuity===

Cantor function: Difference between revisions