Maharam algebra
In mathematics, a Maharam algebra is a complete Boolean algebra with a continuous submeasure. They were introduced by.Definitions
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.Examples
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.
solved a long-standing problem by constructing a Maharam algebra that is not a measure algebra, i.e., that does not admit any countably additive strictly positive finite measure.
