  We study existence and uniqueness of the solution to the gravitational
Vlasov-Poisson system evolving in $\mathbb{R}^3$.
  It is assumed that initially the particles are distributed according to a
spatial density with a power-law decay in space, allowing for unbounded mass,
and an exponential decay in velocities given by a Maxwell-Boltzmann law. We
extend a classical result which holds for systems with finite total mass.
