The dual of the Banach space $C(\Omega)$

Question

It is well-known that the dual of the Banach space $C([0,1])$, i.e. the space of all continuous functions on the interval, is the space of all functions of bounded variation on the interval, $BV([0,1])$. If $\Omega$ is a compact subset of $\mathbb{R}^n$, What is the dual of $C(\Omega)$? How about the dual of all absolutely continuous functions on $\Omega$, $AC(\Omega)$? What do the inner products look like?