Coverings: variations on a result of Rogers and on the Epsilon-net theorem of Haussler and Welzl

Nóra Frankl, János Nagy, Márton Naszódi

We consider four problems. Rogers proved that for any convex body $K$, we can cover ${\mathbb{R}}^d$ by translates of $K$ of density very roughly $d\ln d$. First, we extend this res…