MathGloss

Let $(X,\mathcal T)$ be a Hausdorff topological space and let $\Sigma$ be a σ-algebra containing $\mathcal T$ (so that $\Sigma$ is at least as fine as the Borel σ-algebra on $X$). A measure $\mu$ on $\Sigma$ is locally finite if for all $p \in X$, there exists an open neighborhood $N_p$ of $p$ such that the $\mu$-measure of $N_p$ is finite. That is, $$\forall p \in X, \exists N_p \in T \text{ s.t. } p \in N_p \text{ and } \vert \mu(N_p)\vert < \infty.$$

Wikidata ID: Q2136937

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