Characterizing the range of the complex Monge-Amp\`ere operator
Abstract
In this note, we solve the complex Monge-Amp\`ere equation for measures with a pluripolar part in compact K\"ahler manifolds. This result generalizes the classical results obtained by Cegrell in bounded hyperconvex domains. We also discuss the properties of the complex Monge-Amp\`ere operator in some special cases.
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