A devil's staircase is a function f(x) defined on the interval [a,b] with the following properties:
- f(x) is continuous on [a,b].
- there exists a set N of measure 0 such that for all x outside of N the derivative f ′(x) exists and is zero.
- f(x) is nondecreasing on [a,b].
- f(a) < f(b).