A probabilistic convergence structure assigns a probability
that a given filter converges to a given element of the space.
The role of the

*t*-norm (triangle norm) in the study of
regularity of probabilistic convergence spaces is investigated.
Given a probabilistic convergence space, there exists a finest

*T*-regular
space which is coarser than the given space, and is referred to as
the `

*T*-regular modification'. Moreover, for each probabilistic
convergence space, there is a sequence of spaces, indexed by nonnegative
ordinals, whose first term is the given space and whose last term
is its

*T*-regular modification. The

*T*-regular modification is
illustrated in the example involving `convergence with probability

' for several

*t*-norms. Suitable function space structures
in terms of a given

*t*-norm are also considered.