Abstract
We prove several approximation theorems of the complex Monge–Ampère operator on a compact Kähler manifold. As an application we prove the Cegrell type theorem on a complete description of the range of the complex Monge–Ampère operator in the class of ω-plurisubharmonic functions with vanishing complex Monge–Ampère mass on all pluripolar sets. As a by-product we obtain a stability theorem of solutions of complex Monge–Ampère equations.
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Xing, Y. Continuity of the Complex Monge–Ampère operator on compact Kähler manifolds. Math. Z. 263, 331–344 (2009). https://doi.org/10.1007/s00209-008-0420-8
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DOI: https://doi.org/10.1007/s00209-008-0420-8