Hi,

I need to prove that their exists a Borel measure v on which is absolutely continuous with respect to Lebesgue measure and which satisfies with

I know that the usual Lebesgue measure would satisfy , 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?

Everything I was trying put me in , and I need to be in . Thanks.

*Note I had a typo and edited that the Lebesque measure satisfies