Devil's staircase
In
mathematics, a
devil's staircase is any
function f(x) defined on the
interval [a,b] that has 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).
A standard example of a devil's staircase is the
Cantor function, which is sometimes called "the" devil's staircase. There are, however, other functions that have been given that name. One is defined in terms of the circle map.