It is known that continuous linear functionals on the space $C_0({\mathbb{R}^n})$ are bounded Radon measures ${\cal M}({\mathbb{R}^n})$ where $C_0({\mathbb{R}^n})$ is uniform closure of the space of continuous functions with compact support $C_c({\mathbb{R}^n})$ (for reference e.g. Folland's book on real analysis chapter 7).

I am wondering if there is a similar more general result, namely: what would be a continuous linear function on $C_0({\mathbb{R}^n})$ with values in some Banach space $E$? In analogy with the previous case where we had functionals, I assume it might be in the space of vector-valued bounded Radon measures ${\cal M}({\mathbb{R}^n};E)$?

Radon-Nikodym property. $\endgroup$ – Jochen Wengenroth Dec 2 '13 at 15:25