Inserted: 8 jul 2014
Last Updated: 4 mar 2015
Journal: Comm. Pure Appl. Math.
In this paper we consider an isotropic variant of the $BMO$-type norm recently introduced in a recent work by Bourgain, Brezis and Mironescu. We prove that, when considering characteristic functions of sets, this norm is related to the perimeter. A byproduct of our analysis is a new characterization of the perimeter of sets in terms of this norm, independent of the theory of distributions.