  In this paper we prove that the solutions of the isotropic, spatially
homogeneous Nordheim equation for bosons, with bounded initial, data blow up in
finite time in the $L^\infty$ norm if the values of the energy and particle
density are in the range of values where the corresponding equilibria contains
a Dirac mass. We also prove that, in the weak solutions, whose initial data are
measures with values of particle and energy densities satisfying the previous
condition, a Dirac measure at the origin forms in finite time.
