Lattice Fermions and the Chiral Anomaly

We show in the Wilson model that the contribution of the regular mass term to the four-divergence of the axial vector current in weak coupling perturbation theory is not zero in the chiral limit and is precisely the axial anomaly. Explicit breaking of chiral symmetry in the Wilson term is not relevant for the result. The ABJ anomaly is generated by the fermion mass term also with a chirally symmetric irrelevant term.