Measure algebra

Summary

A measure algebra is a Boolean algebra in which countable suprema exist, together with a countably additive measure that vanishes only at $0$. The main example is the algebra of measurable sets of a measure space modulo null sets. Passing to the measure algebra forgets the points and keeps only what the measure can see. By the isomorphism theorem for measure algebras, all separable atomless probability measure algebras are isomorphic to that of $[0, 1]$.