Question

Cantor function with diffuse measure and singular measure

Answer 1

$\underline\bold\red{Answer}$

The Cantor measure (the probability measure on the real line whose cumulative distribution function is the Cantor function) is an example of a singular continuous measure.

Answer 2

The Cantor measure (the probability measure on the real line whose cumulative distribution function is the Cantor function) is an example of a singular continuous measure.