Uniform approximation of doubly stochastic operators

On the Size of Subclasses of Quasi-Copulas and Their Dedekind–MacNeille Completion

“…In fact, these sets may represent natural frameworks where lattice operations on copulas naturally lie. Our purpose is, hence, to study the relative size of these sets by using the concept of the Baire category as considered, for instance, in [16][17][18][19]. Specifically, we will determine the size of the Dedekind-MacNeille completion of the sets of copulas and supermodular quasi-copulas with respect to the topology induced by the distance (or metric) d ∞ , i.e., the uniform convergence in the set of quasi-copulas.…”