On a problem of von Neumann and Maharam
The 1937 problem of John von Neumann from the Scottish book asks for an algebraic description of measure algebras. In particular, von Neumann conjectured that if a complete Boolean algebra satisfies the countable chain condition and the weak distributive law then it carries a strictly positive countably additive measure. In the 1940's Dorothy Maharam Stone modified the problem, replacing "countably additive measure" by "continuous submeasure", and introduced a technique that uses topology and convergence in Boolean algebras. In my talk I shall describe the recent solution of the von Neumann- Maharam problem (Balcar-Jech-Pazak).