Cutting the same fraction of several measures
classification
🧮 math.MG
math.CO
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measuressamefractiongivenmathbbpositiveproblemssome
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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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