Compactness and $\mathcal D$-Boundedness in Menger's 2-Probabilistic Normed Spaces

P. K Harikrishnan, Bernardo Lafuerza Guillén, K. T. Ravindran

The idea of convex sets and various related results in 2-probabilistic normed spaces were established in [7]. In this paper, we obtain the concepts of convex series closedness, convex series compactness, boundedness and their interrelationships in Menger's 2-probabilistic normed space. Finally, the idea of $\mathcal D$-boundedness in Menger's 2-probabilistic normed spaces and Menger's Generalized 2-Probabilistic Normed spaces are discussed.