Complete ccc Boolean Algebras, The Order Seqential Topology, and a Problem of von Neumann

Abstract

The main (Decomposition) theorem of the article states that for each complete ccc Boolean algebra B either there exists a Maharam submeasure on B, or every nonempty open set in sequential topology on B is topologically dence. The decomposition theorem is further applied to prove the consistency of positive solution to the long open problem of von Neumann