Definition 14.6.1 (Radon Measure). Let $X$ be a LCH space and $\mu: \cb_{X} \to [0, \infty]$ be a Borel measure, then $\mu$ is a Radon measure if:

1. For any $K \subset X$ compact, $\mu(K) < \infty$.

2. $\mu$ is outer regular on all Borel sets.

3. $\mu$ is inner regular on all open sets.