Define
$$\mathcal{F}:=\{f:\mathbb{R}^n\rightarrow[-1,1]:~\mbox{$f$ is measurable and }~\mathrm{E}_{x_1,\ldots, x_n\sim N(0,1)}[|f(x_1,\ldots, x_n)|]\leq c\},$$
where $c<1$ and $x_1,\ldots x_n$ are sampled independently. $\mathcal{F}$ is obviously a convex set. My question is what are the extreme points of $\mathcal{F}$.