Recovery of Rough Sources in the Inverse Monge--Ampère Problem

We prove that every nonnegative source \(f\in L^1(Ω)\) in the Monge--Ampère equation \[ \det D^2u=f\quad\text{in }Ω, \] on a bounded uniformly convex \(C^{1,1}\) domain \(Ω\subset\mathbb R^n\), \(n\geq2\), is uniquely determined by generalized boundary measurements of Alexandrov solutions. The measu