Zero volume boundary for extension domains from Sobolev to BV

In this note, we prove that the boundary of a (W1, p, BV) ( W 1 , p , B V ) -extension domain is of volume zero under the assumption that the domain Ω Ω is 1-fat at almost every x∈ ∂ Ω x ∈ ∂ Ω . Especially, the boundary of any planar (W1, p, BV) ( W 1 , p , B V ) -extension domain is of volume zero.