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In the [3] is proven that almost every, in terms of measure  subsequence  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  subsequence  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  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. 

multiple sequences, statistical convergence.