Two approximation results for divergence free measures

In this paper, we prove two approximation results for divergence free measures. The first is a form of an assertion of J. Bourgain and H. Brezis concerning the approximation of solenoidal charges in the strict topology: Given F ∈ M_b(R^d); R^d/ such that div F = 0 in the sense of distributions, there exist oriented C¹ loops Γi;l with associated measures Γμi;l such that (Formula presented.) weakly-star in the sense of measures and (Formula presented.). The second, which is an almost immediate consequence of the first, is that smooth compactly supported functions are dense in {F ∈ M_b(R^d): div F = 0} with respect to the strict topology.