Comparison principles for Monge-Ampère measures on pluripolar sets

In this paper, we introduce a notion of singularity comparison for plurisubharmonic functions based on the Bedford–Taylor capacity. We establish comparison principles for the complex Monge–Ampère operator on pluripolar sets in the Cegrell classes. As applications, we obtain a characterization of this relation via auxiliary functions in the energy class and prove a corresponding uniqueness result for the Monge–Ampère equation.