Locally finite measure

Let $𝑋$ be a Hausdorff topological space $(𝑋, T)$ and a measure space $(𝑋, Σ, 𝜇)$ at with $Σ$ least as fine as a Borel algebra, i.e. $T \subseteq Σ$ . Then $𝜇$ is locally finite iff every $𝑥 \in 𝑋$ has a neighbourhood $𝑈$ such that $𝜇 (𝑈)$ is finite. measure