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We prove that if $$\{ \varphi _j\}_j$${φj}j is a sequence of subharmonic functions which are increasing to some subharmonic function $$\varphi $$φ in $$\mathbb {C}$$C, then the union of all the weighted Hilbert spaces $$H(\varphi _j)$$H(φj) is dense in the weighted Hilbert space $$H(\varphi )$$H(φ).

Weighted approximation in $$\mathbb {C}$$