Where can I read a proof of the following statement (if it is true).
Let $X$ be a Hausdorff topological space (not necessarily locally compact) and let $\mu$ be a Radon (i.e. locally finite and inner regular) measure defined on the $\sigma$-algebra of Borel subsets of $X$. The measure $\mu$ is determined by the functional $\phi\mapsto\int_{X} \phi d\mu, \phi\in C_{c}(X)$.
I have definitely seen the locally compact case before but I am not sure about the general case. It may be that the proof is really easy.
