  This paper examines asymptotic equivalence in the sense of Le Cam between
density estimation experiments and the accompanying Poisson experiments. The
significance of asymptotic equivalence is that all asymptotically optimal
statistical procedures can be carried over from one experiment to the other.
The equivalence given here is established under a weak assumption on the
parameter space $\mathcal{F}$. In particular, a sharp Besov smoothness
condition is given on $\mathcal{F}$ which is sufficient for Poissonization,
namely, if $\mathcal{F}$ is in a Besov ball $B_{p,q}^{\alpha}(M)$ with $\alpha
p>1/2$. Examples show Poissonization is not possible whenever $\alpha p<1/2$.
In addition, asymptotic equivalence of the density estimation model and the
accompanying Poisson experiment is established for all compact subsets of
$C([0,1]^m)$, a condition which includes all H\"{o}lder balls with smoothness
$\alpha>0$.
