Suppose we're given some sigma-finite measures v1, v2, v3,...
I want to construct [tex]\lambda[/tex] such that vn 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 vn(E) by the measure of the entire space. So, I need to find a more clever way of doing this.