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## Homework Statement

Suppose we're given some sigma-finite measures v

_{1}, v

_{2}, v

_{3},...

I want to construct [tex]\lambda[/tex] such that v

_{n}is absolutely continuous w.r.t. [tex]\lambda[/tex] for all n.

**2. The attempt at a solution**

So far, I've tried thinking of making an infinite weighted (weighted by 2^(-n)). The problem is that sigma-finiteness requires that I can't divide v

_{n}(E) by the measure of the entire space. So, I need to find a more clever way of doing this.