Quaternionic Monge-Ampere operator for unbounded plurisubharmonic functions

In this paper, we generalize the definition of the quaternionic Monge-Ampere operator to some unbounded plurisubharmonic functions, and we prove that the quaternionic Monge-Ampere operator is continuous on the monotonically decreasing sequences of plurisubharmonic functions. After introducing the generalized Lelong number of a positive current, Demailly's comparison theorems are showed. Moreover, we prove that the quaternionic Lelong-Jensen-type formula also holds for the unbounded plurisubharmonic function.