文摘
In this paper, we use the quaternionic closed positive currents to establish some pluripotential results for quaternionic Monge–Ampère operator. By introducing a new quaternionic capacity, we prove a sufficient condition which implies the weak convergence of quaternionic Monge–Ampère measures \((\triangle u_j)^n\rightarrow (\triangle u)^n\). We also obtain an equivalent condition of “convergence in \(C_{n-1}\)-capacity” by using methods from Xing (Proc Am Math Soc 124(2):457–467, 1996). As an application, the range of the quaternionic Monge–Ampère operator is discussed.