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
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