Let $X$ be a set, $\mathcal{A}$ an algebra on $X$. Denote by $B(X, \mathcal{A})$ the Banach space of bounded $\mathcal{A}$-measurable functions with the supremum norm and by $ba(\mathcal{A})$ the Banach space of finitely additive signed measures with bounded variation. Then integration between $B(X, \mathcal{A})$ and $ba(\mathcal{A})$ provides a separating dual pair $\langle B(X, \mathcal{A}), ba(\mathcal{A}) \rangle$ and an isometric isomorphism $B(X, \mathcal{A})' = ba(\mathcal{A})$ of Banach spaces.
Now let $\Sigma$ be a $\sigma$-algebra and consider the subspace $ca(\Sigma) \subseteq ba(\Sigma)$ of countably additive measures. We can look at the dual pair $\langle B(X, \Sigma), ca(\Sigma) \rangle$. We can retrieve $ca(\Sigma)$ as the dual of $B(X, \Sigma)$ by defining on $B(X, \Sigma)$ a locally convex topology weaker than the supremum norm topology. Does anyone know a concrete description of such a topology, especially for the Mackey topology?
Note: Since $ca(\Sigma)$ is a closed subspace of $ba(\Sigma)$, there is another way to create a dual pair with $ca(\Sigma)$, namely with a suitable quotient of $B(X, \Sigma)$. But this is not what I want.
