Locally finite measure

In mathematics, a locally finite measure is a measure for which every point of the measure space has a neighbourhood of finite measure.

Let (X, T) be a Hausdorff topological space and let Σ be a σ-algebra on X that contains the topology T (so that every open set is a measurable set, and Σ is at least as fine as the Borel σ-algebra on X). A measure/signed measure/complex measure μ defined on Σ is called locally finite if, for every point p of the space X, there is an open neighbourhood N_p of p such that the μ-measure of N_p is finite.

In more condensed notation, μ is locally finite if and only if