  Lorentzian versions of classical Riemannian volume comparison theorems by
Gunther, Bishop and Bishop-Gromov, are stated for suitable natural subsets of
general semi-Riemannian manifolds. The problem is more subtle in the
Bishop-Gromov case, which is extensively discussed. For the general
semi-Riemannian case, a local version of the Gunther and Bishop theorems is
given and applied.
