Riesz representation theorem states that, if $\Omega$ is a locally compact Hausdorff space, then $C_0(\Omega)^* = \mathcal{M}(\Omega)$ (or better, they are isomorphic as normed spaces), where $C_0(\Omega)$ is the set of all continuous functions that "vanish at infinity" endowed with the supremum norm, and $\mathcal{M}(\Omega)$ are the (complex) Radon measures on $\Omega$, endowed with the Total variation norm.
Now, say we have a Banach space $X$. We can extend the definition of these objects to $X$-valued maps and measures, say "$C_0(\Omega;X), \mathcal{M}(\Omega;X^*)$" (the definition of the first space seems pretty straightforward; I am not sure how to make sense of the second space but I have seen vector-valued measure defined).
My question would be: do Riesz-type representation theorems exist in this generalized context? Something which could read, for example: $$ C_0(\Omega;X) \simeq \mathcal{M}(\Omega;X^*) \ \ ?$$
Unfortunately, I am not aware if such theory (I have skimmed across a few books, but I never found anything phrased neatly - for example, in terms of duality of normed spaces).
EDIT: I found this post related to my question and also this article
