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A Note on Simultaneous Polar and Cartesian Decomposition

  • F. BartheEmail author
  • M. Csörnyei
  • A. Naor
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1807)

Abstract

We study measures on \(\mathbb{R}^n\) which are product measures for the usual Cartesian product structure of \(\mathbb{R}^n\) as well as for the polar decomposition of \(\mathbb{R}^n\) induced by a convex body. For finite atomic measures and for absolutely continuous measures with density \(d\mu/dx = e^{-V(x)}\), where V is locally integrable, a complete characterization is presented.

Mathematics Subject Classification (2000):

46-06 46B07 52-06 60-06 

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  1. 1.Equipe d’analyse et de Mathématiques appliquéesCNRS-Université de Marne-la-ValléeMarne-la-Vallée, Cedex 2France
  2. 2.Department of MathematicsUniversity College LondonLondonUK
  3. 3.Institute of MathematicsHebrew UniversityJerusalemIsrael

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