  This paper proves the existence of weak solutions to the spatially
homogeneous Boltzmann equation for Maxwellian molecules, when the initial data
are chosen from the space of all Borel probability measures on R^3 with finite
second moments and the (angular) collision kernel satisfies a very weak cutoff
condition. Conservation of momentum and energy is also proved for these weak
solutions, without resorting to any boundedness of the entropy.
