In mathematics, a **locally finite measure** is a measure for which every point of the measure space has a neighbourhood of finite measure.^{[1]}^{[2]}

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

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

- Any probability measure on is locally finite, since it assigns unit measure to the whole space. Similarly, any measure that assigns finite measure to the whole space is locally finite.
- Lebesgue measure on Euclidean space is locally finite.
- By definition, any Radon measure is locally finite.
- The counting measure is sometimes locally finite and sometimes not: the counting measure on the integers with their usual discrete topology is locally finite, but the counting measure on the real line with its usual Borel topology is not.