  In this short note we consider the finite-dimensional distributions of sets
of states generated by dispersing billiards with a random initial condition. We
establish a functional correlation bound on the distance between the
finite-dimensional distributions and corresponding product distributions. We
demonstrate the usefulness of the bound by showing that it implies several
limit theorems. The purpose of this note is to provide a tool facilitating the
study of more general functionals of the billiard process.
