I have the following function (it is a distr. function. Not so important)

It satisfies

for

for all

for

I want to show F is not absolutely continuous w.r.t. Lebesgue measure. Should be straightforward but i dont understand...

It is continuous, but not absolutely continuous.

Apparantly, according to the definition it means the following does not hold: For all exists s.t. whenever a disjoint (finite) sequence of sets with we have .

I can't think of any reason why this is...