Back Teorema del sándwich de jamón Spanish Théorème du sandwich au jambon French Sonkásszendvicstétel Hungarian Teorema del panino al prosciutto Italian ハムサンドイッチの定理 Japanese Теорема о бутерброде Russian Ham sandwich theorem SIMPLE Теорема про бутерброд Ukrainian Định lý bánh mì dăm bông Vietnamese 火腿三明治定理 Chinese
In mathematical measure theory, for every positive integer n the ham sandwich theorem states that given n measurable "objects" in n-dimensional Euclidean space, it is possible to divide each one of them in half (with respect to their measure, e.g. volume) with a single (n − 1)-dimensional hyperplane. This is even possible if the objects overlap.
It was proposed by Hugo Steinhaus and proved by Stefan Banach (explicitly in dimension 3, without taking the trouble to state the theorem in the n-dimensional case), and also years later called the Stone–Tukey theorem after Arthur H. Stone and John Tukey.