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In this paper, we study meromorphic functions on a domain $\Omega \subset\mathbb{C}$ whose image has finite spherical area, counted with multiplicity.The paper is composed of two parts. In the first part, we show that the limitof a sequence of meromorphic functions is naturally defined on $\Omega$ union atree of spheres. In the second part, we show that a set $E \subset \Omega$ isremovable if and only if it is negligible for extremal distance.

On meromorphic functions whose image has finite spherical area