Convex bodies and norms associated to convex measures

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31 Scopus citations


Isotropy-like properties are considered for finite measures with heavy tails. As a basic tool, we extend K. Ball's relationship between convex bodies and finite logarithmically concave measures to a larger class of distributions, satisfying convexity conditions of the Brunn-Minkowski type.

Original languageEnglish (US)
Pages (from-to)303-332
Number of pages30
JournalProbability Theory and Related Fields
Issue number1
StatePublished - Feb 2010

Bibliographical note

Funding Information:
Supported in part by the NSF grant DMS-0706866.


  • Convex measures
  • Floating bodies
  • Isotropic convex bodies


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