  Given an equivalence class $[A]$ in the measure algebra of the Cantor space,
let $\hat\Phi([A])$ be the set of points having density 1 in $A$. Sets of the
form $\hat\Phi([A])$ are called $\mathcal{T}$-regular. We establish several
results about $\mathcal{T}$-regular sets. Among these, we show that
$\mathcal{T}$-regular sets can have any complexity within $\Pi^{0}_{3}$ (=$
\mathbf{F}_{\sigma\delta}$), that is for any $\Pi^{0}_{3}$ subset $X$ of the
Cantor space there is a $\mathcal{T}$-regular set that has the same topological
complexity of $X$. Nevertheless, the generic $\mathcal{T}$-regular set is
$\Pi^{0}_{3}$-complete, meaning that the classes $[A]$ such that
$\hat{\Phi}([A]) $ is $\Pi^{0}_{3}$-complete form a comeagre subset of the
measure algebra. We prove that this set is also dense in the sense of forcing,
as $\mathcal{T}$-regular sets with empty interior turn out to be
$\Pi^{0}_{3}$-complete. Finally we show that the generic $[A]$ does not contain
a $\Delta^{0}_{2}$ set, i.e., a set which is in
$\mathbf{F}_\sigma\cap\mathbf{G}_\delta$
