Selected Proofs on Illumination and Related Topics

Abstract

The proof is based on the following classical theorem of Rogers [217]. We do not prove it here, but instead refer the interested reader to the numerous resources on that, in particular to [219], [1], [143], and [131]. Let $\vartheta$(K) denote the infimum of the densities of coverings of $\mathbb{E}^d$ by translates of the convex body K.