Advertisement

Are All Sets of Positive Measure Essentially Convex?

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

Abstract

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [R-T]
    W. Rhee, M. Talagrand, Packing random items of three colors, Combinatorica 12, 1992, 331–350.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [T-1]
    M. Talagrand, Regularity of Gaussian processes, Acta Math. 159 (1984), 99–149.MathSciNetCrossRefGoogle Scholar
  3. [T-2]
    M. Talagrand, The structure of sign invariant G. B. sets, and of certain gaussian measures, Ann. Probab. 16 (1988), 172–179.MathSciNetzbMATHCrossRefGoogle Scholar

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

Personalised recommendations