Originally Posted by

**Benmath** Hi,

I need to prove that their exists a Borel measure v on $\displaystyle \mathbb{R}^+ $ which is absolutely continuous with respect to Lebesgue measure and which satisfies $\displaystyle v([a,b])=b^2-a^2 $ with $\displaystyle a< b$

I know that the usual Lebesgue measure would satisfy $\displaystyle v([a,b])=b-a $, but I'm terrible at coming up with examples. If I could find one that satisfies the requirement, I'm sure I could prove it is absolutely continuous. Any hints? [/tex]