The usual definition of regularity for convergence spaces can be characterized by a diagonal axiom R due to Cook and Fischer. The generalization of R to the realm of probabilistic convergence spaces depends on a t -norm T, and the resulting axiom R T defines “T-regularity”, which is the primary focus of this paper. We give several characterizations of T-regularity, both in general and for specific choices of T, and investigate some of its basic properties.