Probability approaches to spatially homogeneous Boltzmann equations

This article is devoted to the study of the probability measure solutions to the spatially homogeneous Boltzmann equations. First, we provide a measure theoretical treatment to the Boltzmann collision operator. Then, the existence results both for the cutoff kernels and the non cutoff ones are established in the sense of measure-valued solutions. We also give a partial uniqueness result and some estimates for pth order moment (p2).