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BALANCED CONVEX PARTITIONS OF MEASURES IN ℝd

Part of: Classical measure theory

Published online by Cambridge University Press:  21 October 2011

Pablo Soberón
Pablo Soberón*
Affiliation:
Department of Mathematics, University College London, Gower Sreet, London WC1E 6BT, U.K. (email: [email protected])
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Abstract

We prove the following generalization of the ham sandwich theorem, conjectured by Imre Bárány. Given a positive integer k and d nice measures μ1,μ2,…,μd in ℝd such that μi(ℝd)=k for all i, there is a partition of ℝd into k interior-disjoint convex parts C1,C2,…,Ck such that μi (Cj)=1 for all i,j. If k=2 , this gives the ham sandwich theorem. This result was proved independently by R. N. Karasev.

MSC classification

Secondary: 28A75: Length, area, volume, other geometric measure theory
Type
Research Article
Information
Mathematika , Volume 58 , Issue 1 , January 2012 , pp. 71 - 76
Copyright
Copyright © University College London 2012

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