Cutting the same fraction of several measures

Details Cutting the same fraction of several measures Cutting the same fraction of several measures

2012-03-26

arxiv.org/abs/1203.5591v1

Mathematics

Metric Geometry

7 pages 2 figures

Scientific paper

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

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