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In mathematics, a measure algebra is a Boolean algebra with a countably additive positive measure. A probability measure on a measure space gives a measure algebra on the Boolean algebra of measurable sets modulo null sets. ==Definition== A measure algebra is a Boolean algebra ''B'' with a measure ''m'', which is a real-valued function on ''B'' such that: *''m''(0)=0, ''m''(1)=1 *''m''(''x'') >0 if ''x''≠0 *''m'' is countably additive: ''m''(Σ''x''''i'') = Σ''m''(''x''''i'') if the ''x''''i'' are a countable set of elements that are disjoint (''x''''i'' ∧ ''x''''j''=0 whenever ''i''≠''j''). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Measure algebra」の詳細全文を読む スポンサード リンク
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