Measure algebra

From Wikipedia, the free encyclopedia
Jump to: navigation, search

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[edit]

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: mxi) = Σm(xi) if the xi are a countable set of elements that are disjoint (xixj=0 whenever ij).

References[edit]