  We show that we can obtain a good fit to the present day stellar mass
functions (MFs) of a large sample of young and old Galactic clusters in the
range 0.1 - 10 Msolar with a tapered power law distribution function with an
exponential truncation of the form dN/dm \propto m^alpha [1 -
exp-(m/m_c)^beta]. The average value of the power-law index alpha is -2, that
of beta is 2.5, whereas the characteristic mass m_c is in the range 0.1 - 0.8
Msolar and does not seem to vary in any systematic way with the present cluster
parameters such as metal abundance, total cluster mass or central
concentration. However, m_c shows a remarkable correlation with the dynamical
age of the cluster, namely m_c/Msolar ~ 0.15 + 0.5 tau_dyn^0.75, where tau_dyn
is the dynamical age taken as the ratio of cluster age and dissolution time.
The small scatter seen around this correlation is consistent with the
uncertainties on the estimated value of tau_dyn. We attribute the observed
trend to the onset of mass segregation via two-body relaxation in a tidal
environment, causing the preferential loss of low-mass stars from the cluster
and hence a drift of the characteristic mass m_c towards higher values. If
dynamical evolution is indeed at the origin of the observed trend, it would
seem plausible that high-concentration globular clusters, now with median m_c ~
0.33 Msolar, were born with a stellar MF very similar to that measured today in
the youngest Galactic clusters and with a value of m_c ~ 0.15 Msolar. This
hypothesis is consistent with the absence of a turn-over in the MF of the
Galactic bulge down to the observational limit at ~0.2 Msolar and, if correct,
it would carry the implication that the characteristic mass is not set by the
thermal Jeans mass of the cloud.
