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If Ω is a domain of holomorphy in C, having a compact topological closure into another domain of holomorphy U ⊂ C such that (Ω,U) is a Runge pair, we construct a function F holomorphic in Ω which is singular at every boundary point of Ω and such that F is in L(Ω), for any p ∈ (0, +∞).
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