  We consider the Monge-Amp\`ere equation $\det(D^2u)=f$ in $\mathbb{R}^n$,
where $f$ is a positive bounded periodic function. We prove that $u$ must be
the sum of a quadratic polynomial and a periodic function. For $f\equiv 1$,
this is the classic result by J\"orgens, Calabi and Pogorelov. For $f\in
C^\alpha$, this was proved by Caffarelli and the first named author.

Analysis of PDEs