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 set

Null set

In mathematics, a null set is a set that is negligible in some sense. For different applications, the meaning of "negligible" varies. In measure theory, any set of measure 0 is called a null set...

s.

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(Σx_i) = Σm(x_i) if the x_i are a countable set of elements that are disjoint (x_i ∧ x_j=0 whenever i≠j).