A general Dirichlet problem for the Complex Monge-Ampere operator

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Monge–Ampère measures on pluripolar sets (2007, unknown): “Consider the following two conditions (1) lim z→ζ (u(z) − v(z)) ≥ 0 for every ζ ∈ ∂Ω, (2) u ∈ N (H), v ≤ H.”
Hessian measures on m-polar sets and applications to the complex Hessian equations (2017, background): “4 in [24] shows that there exists a non-negative Radon measure μ such that there does not exist any function u ∈ E that satisfies (ddcu)n = μ.”
A comparison principle for the complex Monge-Ampère operator in Cegrell's classes and applications (2009, background): “He obtained many important results of pluripotential theory in the class E (see [7]–[9]).”
Partial pluricomplex energy and integrability exponents of plurisubharmonic functions (2008, background): “1 in [7] that there exists ψ ∈ F(Ω) with ∫”