Cantor Distribution

This is a continuous distribution.
The Cantor distribution is the probability distribution whose cumulative distribution function is the Cantor function.
This distribution has neither a probability density function nor a probability mass function, as it is not absolutely continuous with respect to Lebesgue measure, nor has it any point-masses.
It is thus neither a discrete nor an absolutely continuous probability distribution, nor is it a mixture of these.
Rather it is an example of a singular distribution

Properties

Assumptions