Measure algebra
Introduction 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'').
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