Are All Sets of Positive Measure Essentially Convex?

  • Michel Talagrand
Part of the Operator Theory Advances and Applications book series (OT, volume 77)


This article discusses the conjecture that roughly speaking, any set A of positive measure is close to a convex set of positive measure, in the sense that such a convex set could be obtained from A using a bounded number of operations. We formulate the conjecture in Gaussian space, and a more special (but more fundamental) version in the set of sequences of zeroes and ones.


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 1995

Authors and Affiliations

  • Michel Talagrand
    • 1
    • 2
  1. 1.Equipe d Analyse-Tour 56 E.R.A. au C.N.R.S. no. 754Université Paris VIParis Cedex 05France
  2. 2.Department of MathematicsThe Ohio State UniversityColumbusUSA

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