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We define probabilistic convergence groups based on Tardiff’s neighborhood systems for probabilistic metric spaces and develop the basic theory. We study, as natural examples, probabilistic metric groups and probabilistic normed groups as well as probabilistic limit groups under a  t -norm as defined earlier by the authors. We further show that a probabilistic convergence group induces a natural probabilistic uniform convergence structure and give a result on probabilistic metrization.

Probabilistic uniformization and probabilistic metrization of probabilistic convergence groups