Uniqueness and sharp boundary estimates for degenerate Monge-Ampère equations with singular measures

We study the uniqueness and boundary behavior of nonzero convex Aleksandrov solutions to $\det D^2 u=M|u|^pν$ with zero boundary values on bounded convex domains in $\mathbb{R}^n (n \geq 2)$. For $0<p<n$, we prove the uniqueness of nonzero convex solutions in the finite-energy class when $ν$ is a lo