In etectrodynamics ($\dim>2$) for free and periodic boundary conditions the asymptotic behavior of the Wilson integral for large contour (loop) perimeters is determined by means of the density with which the contour is smeared over a manifold transversal to the plane of the contour. For two-dimensional electrodynamies with free boundary conditions, Wilson's criterion is satisfied, However, this theory corresponds to a degenerate theory with Wightman functions that vanish identically. The integrals analogous to the Wilson integral are calculated for the Kalb–Ramond model of antisymmetric tensor fields and the theory of a free scalar massless field.