  We present the luminosity function to very faint magnitudes for the globular
clusters in M87, based on a 30 orbit \textit{Hubble Space Telescope (HST)}
WFPC2 imaging program. The very deep images and corresponding improved false
source rejection allow us to probe the mass function further beyond the
turnover than has been done before. We compare our luminosity function to those
that have been observed in the past, and confirm the similarity of the turnover
luminosity between M87 and the Milky Way. We also find with high statistical
significance that the M87 luminosity function is broader than that of the Milky
Way. We discuss how determining the mass function of the cluster system to low
masses can constrain theoretical models of the dynamical evolution of globular
cluster systems. Our mass function is consistent with the dependence of mass
loss on the initial cluster mass given by classical evaporation, and somewhat
inconsistent with newer proposals that have a shallower mass dependence. In
addition, the rate of mass loss is consistent with standard evaporation models,
and not with the much higher rates proposed by some recent studies of very
young cluster systems. We also find that the mass-size relation has very little
slope, indicating that there is almost no increase in the size of a cluster
with increasing mass.
