削减几个措施的同一部分
Cutting the same fraction of several measures
摘要：
研究了如下测度划分问题：用超平面截$\mathbb R^d$中$d+1$测度的相同正分数，或求$\mathbb R^d$的凸子集，使$d+1$在其上具有相同的给定值.对于这两个问题，在一些额外的假设下给出了肯定的答案。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
