Radon Measure on a Metric Space

In the setting of Radon Measures on Locally Compact Metric Spaces: Standing Notation, let $(X,d)$ be a metric space.

(i) Radon measure. A Borel measure $\mu$ on $X$ is a Radon measure if $\mu(K)<\infty$ for every compact $K\subseteq X$, and

$$\mu(B)=\inf\{\mu(V):V\subseteq X\text{ open},\ B\subseteq V\}\qquad(B\in\mathcal{B}(X)),$$ $$\mu(V)=\sup\{\mu(K):K\subseteq X\text{ compact},\ K\subseteq V\}\qquad(V\subseteq X\text{ open}),$$

the infima and suprema being taken in $[0,\infty]$.