  Let $f$ be a multivariate density and $f\_n$ be a kernel estimate of $f$
drawn from the $n$-sample $X\_1,...,X\_n$ of i.i.d. random variables with
density $f$. We compute the asymptotic rate of convergence towards 0 of the
volume of the symmetric difference between the $t$-level set $\{f\geq t\}$ and
its plug-in estimator $\{f\_n\geq t\}$. As a corollary, we obtain the exact
rate of convergence of a plug-in type estimate of the density level set
corresponding to a fixed probability for the law induced by $f$.
