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We study removable sets for the Sobolev space$W$^{1,p}. We show that removability for sets lying in a hyperplane is essentially determined by their thickness measured in terms of a concept of$p$-porosity.
Yurii I. LyubarskiiDepartment of Mathematical Sciences, Norwegian University of Science and TechnologyAlexander RashkovskiiInstitute for Low Temperature Physics & Engineering, 47, Lenin pr., Kharkov, Ukraine