A Cantor function, also known as the Devil's staircase, is a type of continuous and increasing function, but it is not absolutely continuous. It's also a constant on each of the sub-intervals whose interiors produce the complement of the Cantor set.
The Cantor function is an illustration of a singular function and a real function that is uniformly continuous. It has several properties. It's defined everywhere within the interim, and it's increasing. It's not constant but is continuous and differentiable at set interval. The Cantor function is non-decreasing and has a limit of endpoints, and its graph defines a rectifiable curve.