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arXiv · 1203.5591

Cutting the same fraction of several measures

Arseniy Akopyan·Roman Karasev
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Abstract

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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Arseniy Akopyan, Roman Karasev. 2012-05-04. Cutting the same fraction of several measures. https://doi.org/10.1007/s00454-012-9450-4

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