Definition 9.11.276A75EB639CB

Definition 9.11.2.76A75EB639CB An upper semicontinuous function $u:X\to [-\infty ,+\infty )$, not identically $-\infty $ on any nonempty open subset, is $\theta $-plurisubharmonic if it satisfies the following disk condition. For every holomorphic $f:\Delta \to X$, the function $u\circ f+a$ is subharmonic or identically $-\infty $ wherever $a$ is a smooth local potential for $f^*\theta $. The set of these functions is denoted by $\mathrm{PSH}(X,\theta )$.