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High Quality Content by WIKIPEDIA articles! In measure theory, a branch of mathematics, the ham sandwich theorem, also called the Stone Tukey theorem after Arthur H. Stone and John Tukey, states that given any sandwich composed of bread, ham, and cheese, there is a plane that cuts the sandwich into two pieces that contain equal amounts of bread, equal amounts of ham, and equal amounts of cheese. Mathematically, and more generally, given n measurable "objects" in n-dimensional space, it is possible to divide all of them 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.