Continuity of some non-local functionals with respect to a convergence of the underlying measures

We study some non-local functionals on the Sobolev space Wo,p(12) involving a double integral on 12 x12 with respect to a measure mu. We introduce a suitable notion of convergence of measures on product spaces which implies a stability property in the sense of the Gamma-convergence of the corresponding functionals. (c) 2022 Elsevier Masson SAS. All rights reserved.