Affiliation:
1. Department of Mathematics King Saud University Riyadh 11451 Saudi Arabia
2. School of Mechanical Engineering University of Applied Sciences Stralsund , 18435 Stralsund Germany
Abstract
Abstract
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.
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