  We show that the space $\text{Lip}_0(\mathbb R^n)$ is the dual space of
$L^{1}({\mathbb R}^{n}; {\mathbb R}^{n})/N$ where $N$ is the subspace of
$L^{1}({\mathbb R}^{n}; {\mathbb R}^{n})$ consisting of vector fields whose
divergence vanishes. We prove that although the quotient space $L^{1}({\mathbb
R}^{n}; {\mathbb R}^{n})/N$ is weakly sequentially complete, the subspace $N$
is not nicely placed - in other words, its unit ball is not closed for the
topology $\tau_m$ of local convergence in measure. We prove that if $\Omega$ is
a bounded open star-shaped subset of $\mathbb {R}^n$ and $X$ is a closed
subspace of $L^1(\Omega)$ consisting of continuous functions, then the unit
ball of $X$ is compact for the compact-open topology on $\Omega$. It follows in
particular that such spaces $X$, when they have Grothendieck's approximation
property, have unconditional finite-dimensional decompositions and are
isomorphic to weak*-closed subspaces of $l^1$. Numerous examples are provided
where such results apply.
