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CHARACTERIZATION IN TERMS OF MEASURE OF LACUNARY UNIFORM STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES

In the [3] is proven that almost every, in terms of measure , A P subsequence ( ) x S of double sequence S converges to L in the Pringsheim’s sense, if and only if sequence S uniformly statistically converges to L. In this paper, it is proven that analogue is valid and for lacunary uniformly statistical convergence. Almost every, in terms of measure , A P subsequence ( ) x S of double sequence S converges to L in the Pringsheim’s sense, if and only if sequence S lacunary uniformly statistically converges to L. This is not true for measure P. Almost every, in terms of measure P, subsequence ( ) x S of double sequence S of 0’s and 1’s is not almost uniformly statistically convergent, if is sequence S lacunary uniformly statistically convergent and divergent in the Pringsheim’s sense. FIKRET ČUNJALO 26

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