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Cutting the Same Fraction of Several Measures |
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| Authors: | Arseniy Akopyan Roman Karasev |
| Institution: | 1. Institute for Information Transmission Problems RAS, Bolshoy Karetny per. 19, Moscow, 127994, Russia 2. B.N. Delone International Laboratory “Discrete and Computational Geometry”, P.G. Demidov Yaroslavl State University, Sovetskaya st. 14, Yaroslavl’, 150000, Russia 3. Dept. of Mathematics, Moscow Institute of Physics and Technology, Institutskiy per. 9, Dolgoprudny, 141700, Russia |
| Abstract: | We study some measure partition problems: Cut the same positive fraction of d+1 measures in ? d with a hyperplane or find a convex subset of ? 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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