Borel measure that is locally finite but not borel regular

Question

I was wondering if there is an obvious example of a borel measure $\mu$ on $\mathbb{R}^{n}$ that is locally finite but not borel regular, i.e. if there exists $E\subset\mathbb{R}^{n}$, such that for all borel sets $B$ with $E\subset B$ we have $\mu(B)\neq\mu(E)$.