  We study a class of integral functionals known as nonlocal perimeters, which,
intuitively, express a weighted interaction between a set and its complement.
The weight is provided by a positive kernel K, which might be singular. In the
first part of the paper, we show that these functionals are indeed perimeters
in a generalised sense and we establish existence of minimisers for the
corresponding Plateau problem. Also, when K is radial and strictly decreasing,
we prove that halfspaces are minimisers if we prescribe flat boundary
conditions. A Gamma-convergence result is discussed in the second part of the
work. We study the limiting behaviour of the nonlocal perimeters associated
with certain rescalings of a given kernel that has faster-than-L1 decay at
infinity and we show that the Gamma-limit is the classical perimeter, up to a
multiplicative constant that we compute explicitly.
