Let $\mu$ be a regular measure on a locally compact Hausdorff space i.e. $\mu(U)=\sup\{\mu(K):K \ \textrm{is compact}, K\subseteq U\}$ where $U$ is any open set
$\mu(A)=\inf\{\mu(O):O\ \textrm{is open}, O\supset A\}$ where $A$ is any measurable set
$\mu(K) < \infty$ where $K$ is compact
My question : If a measure $\nu$ is absolute continuous wrt $\mu$ namely $\nu=0$ whenever $\mu=0$ and it takes finite values on compact sets, can I say $\nu$ is regular too?
I’m in the answer should be yes but I am not sure. How can I prove or disprove it?
Thanks in advance