Entropy of convex functions on $R^d$

Fuchang Gao, Jon A. Wellner

Let $\Omega$ be a bounded closed convex set in ${\mathbb{R}}^d$ with non-empty interior, and let ${\mathcal{C}}_r(\Omega )$ be the class of convex functions on $\Omega$ with $L^r$-norm bounded by $1$. W…