  Using techniques from infinite ergodic theory, Kessebohmer and Stratmann
determined the asymptotic behavior of the Lebesgue measure of sets of the form
$F^{-n}[\alpha,\beta]$, where $[\alpha,\beta]\subseteq(0,1]$ and $F$ is the
Farey map. In this paper, we provide an effective version of this result,
employing mostly basic properties of the transfer operator of the Farey map and
an application of Freud's effective version of Karamata's Tauberian theorem.
