On limit theorems for random fields - Banys, Rimas (Lietuvos matematikos rinkinys, 2009)
A complete separable metric space of functions defined on the positive quadrant of the plane is constructed. The characteristic property of these functions is that at every point x there exist two lines intersecting at this point such that limits limy→x f (y) exist when y approaches x along any path not intersecting these lines. A criterion of compactness of subsets of this space is obtained.
Keywords: Skorokhod toplogy; weak convergence; tightness; random fields