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ham sandwich theorem
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(Theorem)
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Let $A_1,\ldots,A_m$ be measurable bounded subsets of $\mathbb{R}^m$ . Then there exists an $(m-1)$ -dimensional hyperplane which divides each $A_i$ into two subsets of equal measure.
This theorem has such a colorful name because in the case $m=3$ it can be viewed as cutting a ham sandwich in half. For example, $A_1$ and $A_3$ could be two pieces of bread and $A_2$ a piece of ham. According to this theorem it is possible to make one cut to simultaneously cut all three objects exactly in half.
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"ham sandwich theorem" is owned by mathcam. [ full author list (2) | owner history (1) ]
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Cross-references: objects, theorem, measure, hyperplane, subsets, bounded, measurable
This is version 3 of ham sandwich theorem, born on 2003-10-13, modified 2003-11-24.
Object id is 4772, canonical name is HamSandwichTheorem.
Accessed 5303 times total.
Classification:
| AMS MSC: | 54C99 (General topology :: Maps and general types of spaces defined by maps :: Miscellaneous) |
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Pending Errata and Addenda
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