PROJECTIONS OF BODIES AND HEREDITARY PROPERTIES OF HYPERGRAPHS

We prove that for every n-dimensional body K, there is a rectangular parallelepiped 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 corresponding projection of K. We apply this theorem to projections of finite set systems and to hereditary properties. In particular, we show that every hereditary property of uniform hypergraphs has a limiting density.