Let $\Omega$ be an open subset of $\mathbb{R}^n$ and let $\mu\_1,\, \mu\_2: \mathcal{B}(\Omega)\to [0,\,+\infty]$ be two Radon measure on the Borel algebra. Suppose that for every open set $A$ if $\mu\_1(A)=0$ then $\mu\_2(A)=0$ ( i think with closed sets nothing changes). Is it true that $\mu\_2$ is absolutely continuous with respect to $\mu\_1$ ?

Thanks!