  Kaimanovich and Masur showed that a random walk on the mapping class group
for an initial distribution with finite first moment and whose support
generates a non-elementary subgroup, converges almost surely to a point in the
space PMF of projective measured foliations on the surface. This defines a
harmonic measure on PMF. Here, we show that when the initial distribution has
finite support, the corresponding harmonic measure is singular with respect to
the natural Lebesgue measure on PMF.
