On a measure-theoretic problem of Arveson

Haydon, Richard; Shulman, Victor

doi:10.1090/S0002-9939-96-03076-6

On a measure-theoretic problem of Arveson
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by Richard Haydon and Victor Shulman PDF

Proc. Amer. Math. Soc. 124 (1996), 497-503 Request permission

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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