The de Bruijn-Erdős theorem from a Hausdorff measure point of view

Martin Doležal, Themis Mitsis, Christos Pelekis

Motivated by a well-known result in extremal set theory, due to Nicolaas Govert de Bruijn and Paul Erdős, we consider curves in the unit $n$-cube $[0,1{]}^n$ of the form \[ A=\{(x,f_…