  The goal of this paper is to extend the existence result of measure-valued
solution to the Boltzmann equation in elastic interaction, given by
Morimoto-Wang-Yang, to the inelastic Boltzmann equation with moderately soft
potentials, also as an extensive work of our preceding result in the inelastic
Maxwellian molecules case. We prove the existence and uniqueness of
measure-valued solution under Grad's angular cutoff assumption, as well as the
existence of non-cutoff solution, for both finite and infinite energy initial
datum, by a delicate compactness argument. In addition, the moments propagation
and energy dissipation properties are justified for the obtained measure-valued
solution as well.
