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.

be a Hausdorff topological space and let

that contains the topology

(so that every open set is a measurable set, and

is at least as fine as the Borel

μ

is called locally finite if, for every point

of the space

there is an open neighbourhood

μ

In more condensed notation,

μ

is locally finite if and only if