Remarks about weighted energy integrals over Minkowski spectral functions from Euclidean lattice data

I make some simple observations about the calculation of weighted averages over energy of Minkowski space spectral densities from weighted averages over time of Euclidean space correlation functions, measured in lattice simulations. The correlator of two vector currents is used as an example, where it appears that a determination of a weighted average of the spectral function near the rho pole at the five percent level is possible from lattice simulations.