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Abstract In this note, we prove that the boundary of a (W^1, p, BV) (W 1, p, B V) -extension domain is of volume zero under the assumption that the domain Ω is 1-fat at almost every x x ∈ ∂ Ω. Especially, the boundary of any planar (W^1, p, BV) (W 1, p, B V) -extension domain is of volume zero.
Rajala et al. (Thu,) studied this question.