Pre-dual of the measure space $\mathcal{M}(X)$

Question

I have to find the 'pre-dual of the measure space $\mathcal{M}(X)$'. $X$ can be assumed to be Polish and equipped with the Borel $\sigma$ algebra. This is all I'm given and it's a bit vague. What I found so far is this: if $X$ is locally compact and Hausdorff, then any element in the dual of $C_c(X)$ (the space of continuous compactly supported complex-valued functions on $X$) corresponds to a unique regular Borel measure on $X$, i.e. for $\psi \in (C_c(X))'$, we have $$\psi(f)=\int_X f(x) \,d\mu(x)$$ for such a measure $\mu$. But do we 'hit' all such measures, i.e. can we really identify the dual of $C_c(X)$ with the space of regular Borel measures? Would the mapping $\psi\mapsto\mu$ only be bijective, or can we make it, say, into an isomorphism (using the total variation norm)? Is there another space whose dual is the space of all Borel measures on $X$, without making the assumptions that $X$ is locally compact and Hausdorff? (Also, if you know good literature on this please let me know, I was having a hard time finding something.) (Edit: for anyone interested (and German speaking): Funktionalanalysis by Dirk Werner seems to cover the topic well.)