Completion of probabilistic uniform limit spaces

In this article completions of special probabilistic semiuniform convergence spaces are considered. It turns out that every probabilitic Cauchy space under a given t-norm T (triangular norm) has a completion which, in the special case of probabilistic Cauchy spaces with reference to T = min, coincides with the Kent-Richardson completion for probabilistic Cauchy spaces. Moreover, a completion of probabilistic uniform limit spaces T = min is given which in case of constant probabilistic uniform limit spaces coincides with the Wyler completion. Mathematics Subject Classification (2000): 54A20, 54E15, 54D35 Quaestiones Mathematicae 25 (2002), 125-14