I know that, a measure $\nu$ is absolutely continuous with respect to another measure $\mu$ if $\mu(A)=0$ implies $\nu(A)=0$. and the relation is indicated by $\nu<<\mu$.
On the other hand, measures $\mu$ and $\nu$ are mutually singular if they have disjoint support. that is, there exist set $S_\mu$ and $S_\nu$ such that
$$
S_\mu \cap S_\nu=\emptyset,\\
\mu(\Omega-S_\mu)=0, \\
\nu(\Omega-S_\nu)=0.
$$
My question is that, do these concepts coincide (in some case)? I mean, given singularity, is it possible to get absolute continuity (or vice versa)?
Thank you