Lacunary ideal convergence of multiple sequences in probabilistic normed spaces

An ideal II is a family of subsets of positive integers N×NN×N which is closed under finite unions and subsets of its elements. The aim of this paper is to study the notion of lacunary II-convergence of double sequences in probabilistic normed spaces as a variant of the notion of ideal convergence. Also lacunary II-limit points and lacunary II-cluster points have been defined and the relation between them has been established. Furthermore, lacunary-Cauchy and lacunary II-Cauchy, lacunary I*I*-Cauchy, lacunary I*I*-convergent double sequences are introduced and studied in probabilistic normed spaces. Finally, we provided example which shows that our method of convergence in probabilistic normed space is more general.