Weak convergence and solvability of the non-polar part NP (ddc•)n of Monge-Ampère measures in the class D(Ω)
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Abstract
The aim of this note is to prove weak convergence in the class $\mathcal{D}(\O)$ and of the corresponding non-polar part $(NP)(dd^c\bullet)^n$ of Monge-Amp\`ere measures in the relationship with the convergence in $C_n$-capacity on an open subset $\O$ of $\mathbb{C}^n$. In the end of the note we investigate the solvability of the Monge--Amp\`ere equation for the non-polar part in the class $\mathcal{D}(\Omega)$
Keywords
class $\mathcal{D}(\Omega)$, convergence in capacity, weak convergence of the complex Monge-Amp\`ere measures, weak convergence of the non-polar part, solvability of the non-polar part of the complex Monge-Amp\`ere measure
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References
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