  We introduce a notion of non-local perimeter which is defined through an
arbitrary positive Borel measure on $\mathbb{R}^d$ which integrates the
function $1\wedge |x|$. Such definition of non-local perimeter encompasses a
wide range of perimeters which have been already studied in the literature,
including fractional perimeters and anisotropic fractional perimeters. The main
part of the article is devoted to the study of the asymptotic behaviour of
non-local perimeters. As direct applications we recover well-known convergence
results for fractional perimeters and anisotropic fractional perimeters
