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Convex bodies and norms associated to convex measures
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  • Published: 04 March 2009

Convex bodies and norms associated to convex measures

  • Sergey G. Bobkov1 

Probability Theory and Related Fields volume 147, pages 303–332 (2010)Cite this article

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, Vincent Hall 228, 206 Church St SE, Minneapolis, MN, 55455, USA

    Sergey G. Bobkov

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  1. Sergey G. Bobkov
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Correspondence to Sergey G. Bobkov.

Additional information

Supported in part by the NSF grant DMS-0706866.

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Bobkov, S.G. Convex bodies and norms associated to convex measures. Probab. Theory Relat. Fields 147, 303–332 (2010). https://doi.org/10.1007/s00440-009-0209-7

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  • Received: 09 May 2008

  • Revised: 06 February 2009

  • Published: 04 March 2009

  • Issue Date: May 2010

  • DOI: https://doi.org/10.1007/s00440-009-0209-7

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Keywords

  • Convex measures
  • Isotropic convex bodies
  • Floating bodies

Mathematics Subject Classification (2000)

  • Primary 60xx
  • Secondary 46xx
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