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(Σxi) = Σm(xi) if the xi are a countable set of elements that are disjoint (xi ∧ xj=0 whenever i≠j).

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

Hellenica World - Scientific Library

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