Abstract
In the paper we introduce weighted energy classes $${\mathcal {E}}_{\chi }(\varOmega )$$ of plurifinely plurisubharmonic functions on a bounded $${\mathcal {F}}$$-hyperconvex domain $$\varOmega $$ in $${\mathbb {C}}^n$$ and prove the existence of weak solutions of the equation of complex Monge–Ampere type in this class.
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