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On a measure-theoretic problem of Arveson
Authors:Richard Haydon  Victor Shulman
Institution:Brasenose College, Oxford OX1 4AJ, United Kingdom ; Polytechnic Institute, Lenina Street, 16000 Vologda, Russia
Abstract:A probability measure $\nu $ on a product space $X\times Y$ is said to be bistochastic with respect to measures $\lambda $ on $X$ and $\mu $ on $Y$ if the marginals $\pi _1(\nu )$ and $\pi _2(\mu ) $ are exactly $\lambda $ and $\mu $. A solution is presented to a problem of Arveson about sets which are of measure zero for all such $\nu $.

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