  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 $F \in M_b(\mathbb{R}^d;\mathbb{R}^d)$ such that $\operatorname*{div}
F=0$ in the sense of distributions, there exist oriented $C^1$ loops
$\Gamma_{i,l}$ with associated measures $\mu_{\Gamma_{i,l}}$ such that \[ F=
\lim_{l \to \infty} \frac{\|F\|_{M_b(\mathbb{R}^d;\mathbb{R}^d)}}{n_l \cdot l}
\sum_{i=1}^{n_l} \mu_{\Gamma_{i,l}} \] weakly-star in the sense of measures and
\[ \lim_{l \to \infty} \frac{1}{n_l \cdot l} \sum_{i=1}^{n_l}
\|\mu_{\Gamma_{i,l}}\|_{M_b(\mathbb{R}^d;\mathbb{R}^d)} = 1. \] The second,
which is an almost immediate consequence of the first, is that smooth compactly
supported functions are dense in \[ \left\{ F \in
M_b(\mathbb{R}^d;\mathbb{R}^d): \operatorname*{div}F=0 \right\} \] with respect
to the strict topology.
