Theorem 14.5.4. Let $X$ be a topological space and $\mu: \cb_{X} \to [0, \infty]$ be a Borel measure. If:

1. $X$ is a LCH space.

2. Every open set of $X$ is $\sigma$-compact.

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

then $\mu$ is a regular measure.