Some reference is Exercise 84 (Cantor function) in Tao's lecture notes at https://terrytao.wordpress.com/2010/10/16/245a-notes-5-diffe...

The results before/after that result have other niceties: a one sided fundamental theorem of calculus for monotone functions (even though the Cantor function has 0 derivative!) or the fact that monotone functions can also be decomposed as the sum of continuous monotone function and a jump function such as Cantor's function.