Abstract
The aim of this paper is to introduce and study the notion ofI-convergence of random variables via probabilistic norms. Furthermore, we introduceI-convergence inLpspace and establish some interesting results.
Highlights
Fast [1] and Steinhaus [2] independently introduced the notion of statistical convergence for sequences of real numbers, which is a generalization of the concept of convergence
Kostyrko et al [11] presented a generalization of the concept of statistical convergence with the help of ideal I of subsets of the set of natural numbers N and further studied in [12,13,14,15,16]
By using the concept of Menger, Serstnev [18] introduced the concept of probabilistic normed space, which is an important generalization of deterministic results of linear normed spaces
Summary
Fast [1] and Steinhaus [2] independently introduced the notion of statistical convergence for sequences of real numbers, which is a generalization of the concept of convergence. Kostyrko et al [11] presented a generalization of the concept of statistical convergence with the help of ideal I of subsets of the set of natural numbers N and further studied in [12,13,14,15,16]. The concept of ideal convergence for single and double sequence of real numbers in probabilistic normed space was introduced and studied by Mursaleen and Mohiuddine [21, 22]. Mohiuddine et al [24] studied the notion of ideal convergence for single and double sequences in random 2normed spaces, respectively. For more detail and related concept, we refer to [25,26,27,28,29,30,31,32,33] and references therein
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