  (Abridged) Accurate luminosity functions (LF) for a dozen globular clusters
have now been measured at or just beyond their half-light radius using HST.
They span almost the entire cluster main sequence below ~ 0.75 Msolar. All
these clusters exhibit LF that rise continuously from an absolute I magnitude
M_I ~ 6 to a peak at M_I ~ 8.5-9 and then drop with increasing M_I.
Transformation of the LF into mass functions (MF) by means of the most recent
mass luminosity relations that are consistent with all presently available data
on the physical properties of low mass, low metallicity stars shows that all
the LF observed so far can be obtained from MF having the shape of a log-normal
distribution with characteristic mass m_c=0.33 +/- 0.03 Msolar and standard
deviation sigma = 1.81 +/- 0.19. After correction for the effects of mass
segregation, the variation of the ratio of the number of higher to lower mass
stars with cluster mass or any simple orbital parameter or the expected time to
disruption recently computed for these clusters shows no statistically
significant trend over a range of this last parameter of more than a factor of
100. We conclude that the global MF of these clusters have not been measurably
modified by evaporation and tidal interactions with the Galaxy and, thus,
should reflect the initial distribution of stellar masses. Since the log-normal
function that we find is also very similar to the one obtained independently
for much younger clusters and to the form expected theoretically, the
implication seems to be unavoidable that it represents the true stellar IMF for
this type of stars in this mass range.
