## On a problem of von Neumann and Maharam

## T.Jech(logic seminar)

Abstract:

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).