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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.
==Definition==
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
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抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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