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Archiv der Mathematik

, Volume 92, Issue 4, pp 366–376 | Cite as

On the Yao-Yao partition theorem

  • Joseph Lehec
Article

Abstract.

The Yao-Yao partition theorem states that for any probability measure μ on \({\mathbb{R}}^n\) having a density which is continuous and bounded away from 0, it is possible to partition \({\mathbb{R}}^n\) into 2 n regions of equal measure for μ in such a way that every affine hyperplane of \({\mathbb{R}}^n\) avoids at least one of the regions. We give a constructive proof of this result and extend it to slightly more general measures.

Mathematics Subject Classification (2000).

52C99 

Keywords.

Discrete geometry equipartitions 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Université Paris-Est, Laboratoire d’Analyse et de Mathématiques appliquéesMarne la Vallée Cedex 2France

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