Statistical convergence in probabilistic generalized metric spaces w.r.t. strong topology

Abstract

Abstract In this paper, the concept of probabilistic g-metric space with degree l, which is a generalization of probabilistic G-metric space, is introduced. Then, by endowing strong topology, the definition of l-dimensional asymptotic density of a subset A of N l $\mathbb{N}^{l}$ is used to introduce a statistically convergent and Cauchy sequence and to study some basic facts.

Keywords

• Probabilistic metric space
• Generalized metric space
• Statistical convergence
• Statistical Cauchy sequence
• Strong topology