I-statistical limit points and I-statistical cluster points of double sequences

In this paper we extend the notions of statistical limit points and statistical cluster points of double sequences of real numbers to I-statistical limit points and I-statistical cluster points of double sequences of real numbers. We study some basic properties of the set of all I-statistical cluster points and the set of all I-statistical limit points of a double sequence of real numbers including their interrelationship. Also introducing additive property of double I-natural density zero sets we present I-statistical analogue of some well known theorems concerning double sequences that are equivalent to the completeness of the real line.