[[Measure theory MOC]]
# Locally finite measure

Let $X$ be a [[Hausdorff space|Hausdorff]] [[topological space]] $(X, \mathcal{T})$ and a [[measure space]] $(X, \Sigma, \mu)$ at with $\Sigma$ least as fine as a [[Borel set|Borel algebra]], i.e. $\mathcal{T} \sube \Sigma$.
Then $\mu$ is **locally finite** iff every $x \in X$ has a neighbourhood $U$ such that $\mu(U)$ is finite. #m/def/measure

## Properties

- [[Local finite measure of a compact set is finite]]

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