Approximation of homogeneous measures in the 2-Wasserstein metric

It is shown that, on certain weighted spaces of vector fields on R3, any homogeneous measure of finite energy density and dissipation can be approximated in the second Wasserstein distance by homogeneous measures supported by finite trigonometric polynomials of increasing period and degree. In particular, the periodic correlation functions of the approximation converge uniformly on compact sets of R3 to the correlation function of the given measure.