Discrete & Computational Geometry

, Volume 49, Issue 2, pp 402–410 | Cite as

Cutting the Same Fraction of Several Measures



We study some measure partition problems: Cut the same positive fraction of d+1 measures in ℝd with a hyperplane or find a convex subset of ℝd on which d+1 given measures have the same prescribed value. For both problems positive answers are given under some additional assumptions.


The ham sandwich theorem Balanced partition 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Institute for Information Transmission Problems RASMoscowRussia
  2. 2.B.N. Delone International Laboratory “Discrete and Computational Geometry”P.G. Demidov Yaroslavl State UniversityYaroslavl’Russia
  3. 3.Dept. of MathematicsMoscow Institute of Physics and TechnologyDolgoprudnyRussia

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