  Let $R$ be a Mori domain with complete integral closure $\widehat R$, nonzero
conductor $\mathfrak f = (R \ :\ \widehat R)$, and suppose that both $v$-class
groups $\mathcal C_v (R)$ and $\mathcal C_v (\widehat R)$ are finite. If
$R/\mathfrak f$ is finite, then the elasticity of $R$ is either rational or
infinite. If $R/\mathfrak f$ is artinian, then unions of sets of lengths of $R$
are almost arithmetical progressions with the same difference and global bound.
We derive our results in the setting of $v$-noetherian monoids.
