Maharam algebra

In mathematics, a Maharam algebra is a complete Boolean algebra with a continuous submeasure. They were introduced by Maharam (1947).

A continuous submeasure or Maharam submeasure on a Boolean algebra is a real-valued function m such that

A Maharam algebra is a complete Boolean algebra with a continuous submeasure.

Every probability measure is a continuous submeasure, so as the corresponding Boolean algebra of measurable sets modulo measure zero sets is complete it is a Maharam algebra.