Absolute Continuity: Showing f is Increasing on [a,b]

[sbashrawi]

Homework Statement

show that if f is increasing on
[a, b], then f is absolutely continuous if and only if for each $$\epsilon$$ > 0 there
is a $$\delta$$ > 0 such that for each measurable subset E of [a, b],
m*(f(E)) < $$\epsilon$$ if m(E) < $$\delta$$.

Homework Equations

The Attempt at a Solution

 

[ystael]

and ... ? What have you tried so far? What do you have trouble understanding?