This is a quote from the wikipedia entry on regular measures:
Any Borel probability measure on a locally compact Hausdorff space with a countable base for its topology ... is regular.
Is this actually true? If so could someone point me to a reference where I could find a proof of the statement?
Edit: I should add that the definition of regularity used in wikipedia is that $\mu$ is regular if
$$\mu(A)=\sup\{\mu(F):F\subset A\text{ and $F$ is compact}\}=\inf\{\mu(B):A\subset B\text{ and $B$ is open}\}$$
where the infimum/supremum is taken over the space's Borel sigma algebra.