Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On a measure-theoretic problem of Arveson


Authors: Richard Haydon and Victor Shulman
Journal: Proc. Amer. Math. Soc. 124 (1996), 497-503
MSC (1991): Primary 28A35; Secondary 28A12, 47D25
DOI: https://doi.org/10.1090/S0002-9939-96-03076-6
MathSciNet review: 1301501
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 $.


References [Enhancements On Off] (What's this?)

  • 1 W. Arveson, Operator algebras and invariant subspaces, Ann. of Math. 100 (1974), 433--533, MR 51:1420.
  • 2 G. Choquet, Theory of capacities, Ann. Inst. Fourier, Grenoble 5 (1953), 131--295, MR 18:295g.
  • 3 ------, Forme abstraite du théorème de capacitabilité, Ann. Inst. Fourier, Grenoble 5 (1959), 131--295, MR 22:3692b.
  • 4 C. Dellacherie and J.-P. Meyer, Probabilités et Potentiel, Hermann, Paris, 1966, MR 58:7757.
  • 5 C.A. Rogers et al., Analytic Sets, Academic Press, London, 1980.
  • 6 L. Schwartz, Radon measures on arbitrary topological spaces and cylindrical measures, Oxford University Press/Tata Institute, 1973, MR 54:14030.
  • 7 V.N. Sudakov, Geometric problems of the theory of infinite-dimensional probability distributions, Trudy Mat. Inst. Steklov 141 (1976)=Proceedings of the Steklov Institute (1979), MR 55:4359.
  • 8 F. Topsøe, A criterion for weak convergence of measures with an application to measures on $D[0,1]$, Math. Scand. 25 (1969), 97--104, MR 40:8117.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 28A35, 28A12, 47D25

Retrieve articles in all journals with MSC (1991): 28A35, 28A12, 47D25


Additional Information

Richard Haydon
Affiliation: Brasenose College, Oxford OX1 4AJ, United Kingdom
Email: richard.haydon@brasenose.oxford.ac.uk

Victor Shulman
Affiliation: Polytechnic Institute, Lenina Street, 16000 Vologda, Russia
Email: vagor@vpi.vologda.su

DOI: https://doi.org/10.1090/S0002-9939-96-03076-6
Received by editor(s): August 29, 1994
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society