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 n measurable "objects" in n-dimensional space, it is possible to divide all of them in half (with respect to their measure, i.e. 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.
Read more about Ham Sandwich Theorem: Naming, History, Reduction To The Borsuk–Ulam Theorem, Measure Theoretic Versions, Discrete and Computational Geometry Versions
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