 Monotonicity of the normalized extremal number

For every fixed graph $H$, the sequenceis nonincreasing once $n\ge 2$. Indeed, choose a uniformly random $m$-vertex induced subgraph of an extremal $H$-free graph on $n$ vertices. It remains $H$-free and has expected edge countwhich cannot exceed $\mathrm{ex}(m,H)$.