A general formula for the anisotropic outer Minkowski content of a set

We generalize to the anisotropic case some classical and recent results on the (n - 1)-Minkowski content of rectifiable sets in Rn, and on the outer Minkowski content of subsets of Rn. In particular, a general formula for the anisotropic outer Minkowski content is provided; it applies to a wide class of sets that are stable under finite unions.