W2,1+ε estimates for the Monge–Ampère equation

We study strictly convex Alexandrov solutions uu of the real Monge–Ampère equation det(∇2u)=fdet(∇2u)=f, where ff is measurable, positive, and bounded away from 0 and ∞∞. Under only these assumptions we prove interior W2,1+ε-regularity of uu.