  We discuss the two-point functions of the U(1) current and energy-momentum
tensor in certain gapped three-dimensional field theories, and show that the
parity-odd part in both of these correlation functions is one-loop exact. In
particular, we find a new and simplified derivation of the Coleman-Hill theorem
that also clarifies several subtleties in the original argument. For the energy
momentum tensor, our result means that the gravitational Chern-Simons term for
the background metric does not receive quantum corrections
