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Ham sandwich theorem



In measure theory, a branch of mathematics, the ham sandwich theorem, also called the Stone–Tukey theorem after Marshall Stone and John Tukey, states that given n "objects" in n-dimensional space, it is possible to divide each one in half (according to volume) with a single (n − 1)-dimensional hyperplane. Here the "objects" should be sets of finite measure (or, in fact, just of finite outer measure) for the notion of "dividing the volume in half" to make sense.



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