Can a small Gaussian perturbation break subadditivity?

Paolo Leonetti

Given an integer $a\ge 1$, a function $f:\mathbb{R}\to \mathbb{R}$ is said to be $a$-subadditive if $$f(ax+y)\le af(x)+f(y)\text{ for all }x,y\in \mathbb{R}.$$ Of cours…