rca$(X)=$$C_0(X)$$^*$ if $X$ is locally compact Hausdorff.
What other Banach spaces of measures are duals of function Banach spaces?
Such as ca$(X)$ or ba$(X)$ or rca$(X)$ under more general (or incomparable) assumptions. With the total variation norm.
Preferably the function space would be separable and include $1$ (i.e., the constants). Preferably provide a reference (and the assumptions on $X$).
The above rca result is about countably-additive measures (Rudin:RCA, 6.19), but also results on finitely-additive measures are welcome (to a lesser extent also the vector-valued ones).
[Note: $C_0(X)$ is separable but does not include $1$ unless $X$ is compact. $Y = C_0(X)+\mathbb K$ with the sup-norm satisfies both criteria but requires us to add one finitely-additive measure to the basis of the measure space to make it the dual space. So does any other extension to $C_0(X)$ too, by the Hahn-Banach theorem. So we should, rather, replace $C_0(X)$ by something else if we want to keep both spaces canonical ones, such as rca$(X)$. Are there such results? $C(X)$ tends to be non-separable.]
ba$(X)$ is the dual of the set $B(X)$ of bounded measurable functions on an algebra $\Sigma$ on a set $X$. $B$ contains $1$ (but is not separable unless $\Sigma$ is finite?). Similarly, $L^\infty(\mu)^*$ consists of $\mu$-a.c. elements of ba$(X)$, but also $L^\infty$ tends to be nonseparable. Does either have a nice (somehow standard or "canonical") subspace that is the dual of a separable normed space?
Above the scalar field $\mathbb K$ may be $\mathbb R$ or $\mathbb C$. I'm interested in $\mathbb R$ but other readers may appreciate $\mathbb C$ results too.