ω-pluripolar sets and subextension of ω-plurisubharmonic functions on compact Kähler manifolds

Uniqueness in E(X,ω)

“…In the class D a (X, ω) the partial comparison principle (for n − k = 1) was proven in [17]. In particular the result holds for bounded u, v and φ j , j = 1, .…”

“…Note that all the functions which appear in the wedge products belong to D a (X, ω), hence [17] applies. So, for u, v bounded we have…”

“…Please note that the terminology in the Cegrell classes, partially due to the mentioned differences in the "local" and "global" settings varies in the literature. In particular the class D(X, ω) is denoted by E(X, ω) in [17] or [13]. The class E(X, ω) in turn differs in some aspects from the class E(Ω) in the "flat" setting (for example a function in E(Ω) may have a Monge-Ampère measure that charges points).…”