Abstract. In this work, using the concept of I-convergence and using the concept of rough convergence, we introduced the notion of rough I-convergence and the set of rough I-limit points of a sequence and obtained two rough I-convergence criteria associated with this set. Later, we proved that this set is closed and convex. Finally, we examined the relations between the set of I-cluster points and the set of rough I-limit points of a sequence. Background and introductionThe concept of convergence of a sequence of real numbers has been extended to statistical convergence independently by Fast [4] [14]. In general, statistically convergent sequences satisfy many of the properties of ordinary convergent sequences in metric spaces.The idea of I-convergence was introduced by Kostyrko et al.[6] as a generalization of statistical convergence which is based on the structure of the ideal I of subset of the set of natural numbers. Nuray and Ruckle [9] indepedently introduced the same with another name generalized statistical convergence. Kostyrko et al. [7] studied the idea of I-convergence and extremal I-limit points and Demirci [3] studied the concepts of I-limit superior and limit inferior.Salát, Tripathy and Ziman [13] introduced the notion of c I A and m I A , the I-convergence field and bounded I-convergence field of an infinite matrix A.The idea of rough convergence was first introduced by Phu [10] in finitedimensional normed spaces. In [10], he showed that the set LIM r x is bounded, closed, and convex; and he introduced the notion of rough Cauchy sequence. He also investigated the relations between rough convergence and other 2010 Mathematics Subject Classification: 40A05, 40A35.

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The concept of statistical convergence was presented by Steinhaus in 1951. This concept was extended to the double sequences by Mursaleen and Edely in 2003. Throughout this paper we will present multidimensional analogues of the results presented by Fridy and Orhan in 1997. To achieve this goal multidimensional analogues of the definition for bounded statistically sequences, statistical inferior and statistical superior will be presented. In addition to these results we will investigate statistical core for double sequences and study an inequality related to the statistical and P -cores of bounded double sequences.

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