Let $\mathcal{X}$ be a compact of $\mathbb{R}^d$, let $\mathcal{M(X)}$ be the space of Radon measures defined as the topological dual of the space of continuous functions.
Consider now the space of vector Radon measures, denoted $\mathcal{M(X)}^d$. Any $\nu \in \mathcal{M(X)}^d$ has a divergence $\text{div}(\nu) = \sum_{i=1}^d \partial_i \nu$ which might or might not be a Radon measure i.e. $\text{div}(\nu) \in \mathcal{M(X)}$.
I'm looking for any functional analysis tools helping me to find the dual (or predual whatever) of the space $\left\{\nu \in \mathcal{M(X)}^d, \text{s.t. } \text{div}(\nu) \in \mathcal{M(X)}\right\}$.