PROJECTIONS OF BODIES AND HEREDITARY PROPERTIES OF HYPERGRAPHS

We prove that for every n-dimensional body K, there is a rectangular p arallelepiped B of the same volume as K, such that the projection of B onto any coordinate subspace is at most as large as that of the corre sponding projection of K. We apply this theorem to projections of fini te set systems and to hereditary properties. In particular, we show th at every hereditary property of uniform hypergraphs has a limiting den sity.