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The well-known Thullen-Remmert-Stein's theorem (, ) asserts that, for a domainDinCNand ann-dimensional irreducible analytic setSinD, a purely n-dimensional analytic setAinD—Shas an essential singularity at any point in 5 ifAhas at least one essential singularity in S. In , E. Bishop generalized this to the case thatAhas the boundary of capacity zero in his sense. Afterwards, in , W. Rothstein obtained more precise informations on the essential singularities ofAunder the assumptiondoi:10.1017/s0027763000014501 fatcat:obx4yeskr5cvzeek5pwrjudxu4