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We introduce a weighted version of the pluripotential theory on complexK\"{a}hler manifolds developed by Guedj and Zeriahi. We give the appropriatedefinition of a weighted pluricomplex Green function, its basic properties andconsider its behaviour under holomorphic maps. We also establish ageneralization of Siciak's H-principle.

Weighted pluripotential theory on complex K\"{a}hler manifolds