On a measure-theoretic problem of Arveson

Abstract

A probability measure ν \nu on a product space X × Y X\times Y is said to be bistochastic with respect to measures λ \lambda on X X and μ \mu on Y Y if the marginals π 1 ( ν ) \pi _1(\nu ) and π 2 ( μ ) \pi _2(\mu ) are exactly λ \lambda and μ \mu . A solution is presented to a problem of Arveson about sets which are of measure zero for all such ν \nu .