Lorentzian versions of classical Riemannian volume comparison theorems by Günther, 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 Günther and Bishop theorems is given and applied.
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Ehrlich et al. (2000) studied this question.
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