Intervals of uniform Turán densities

Abstract

We prove that the set ${\Pi }_{\therefore ,\infty }$ of uniform Turán densities of possibly infinite families of $3$-graphs contains a terminal interval: there exists $\delta >0$ such that $[1-\delta ,1]\subseteq {\Pi }_{\therefore ,\infty }$. Consequently, ${\Pi }_{\therefore ,\infty }$ has positive Lebesgue measure and Hausdorff dimension $1$.

arXiv comment19pp, comments are welcome