In mathematics, a measure algebra is a Boolean algebra with a countably additive positive measure.

Several further properties can be derived from the definition of a countably additive measure.

Another generalization is the finitely additive measure, which are sometimes called contents.

Let be a measure space and the real space of signed -additive measures on .

Note that the proof of theorem 2 is largely dependent on the fact that non-negative additive measures are monotone.

The φ-measurable sets form a σ-algebra and φ restricted to the measurable sets is a countably additive complete measure.

An ultrafilter may be considered as a finitely additive measure.

If Σ is a sigma-algebra, then the space is defined as the subset of consisting of countably additive measures.

To explain this a bit more, the question of whether a finitely additive measure exists, that is preserved under certain transformations, depends on what transformations are allowed.

She pioneered the research of finitely additive measures on integers.