A continuous analogue of Erdős' $k$-Sperner theorem

Themis Mitsis, Christos Pelekis, Václav Vlasák

A \emph{chain} in the unit $n$-cube is a set $C\subset [0,1{]}^n$ such that for every $\mathbf{x}=(x_1,\dots ,x_n)$ and $\mathbf{y}=(y_1,\dots ,y_n)$ in $C$ we either have $x_i\le y_…