  We show that recent observations of fractal dimensions in the $\mu$-space of
$N$-body Hamiltonian systems with long-range interactions are due to finite $N$
and finite resolution effects. We provide strong numerical evidence that, in
the continuum (Vlasov) limit, a set which initially is not a fractal (e.g. a
line in 2D) remains such for all finite times. We perform this analysis for the
Hamiltonian Mean Field (HMF) model, which describes the motion of a system of
$N$ fully coupled rotors. The analysis can be indirectly confirmed by studying
the evolution of a large set of initial points for the Chirikov standard map.
