The pluripolar parts of the Monge–Ampère measures of $\mathcal F$-plurisubharmonic functions

We introduce the notion of complex Monge–Ampère measures for a subclass of the class of unbounded $\mathcal F$-plurisubharmonic functions. This generalizes classical results by Cegrell [Ann. Inst. Fourier (Grenoble) 54 (2004), 159–179] who introduced the complex Monge–Ampère operator for unbounded plurisubharmonic functions.