Definition 20.1.1 (Radon Measure).label 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. (R1)

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

2. (R2)

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

3. (R3’)

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