A question on finitely additive measures by Peter Biryukov and Valery Mishkin

Topology Atlas Document # qaaa-12 | Production Editor: Harriet Lord

Question
A question on finitely additive measures
Peter Biryukov and Valery Mishkin

Does there exist a non-atomic charge (finitely additive measure) \nu on P(\omega) vanishing at each point such that for every A,B \in P(\omega) with 0 < \nu(A) < 1 and 0 < \nu(B) < 1 there is a non-singular transformation (i.e. leaving the null ideal invariant) f \in Sym(\omega) such that f(A) = B ?

Received by the editors: November 24, 1997