Lacunary statistical convergence of multiple sequences

Quite recently, Mursaleen and Edely [M. Mursaleen, O.H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. (in press)], defined the statistical analogue for double sequences x={xk,l}x={xk,l} as follows: A real double sequence x={xk,l}x={xk,l} is said to be P-statistically convergent to LL provided that for each ϵ>0ϵ>0P−limm,n1mn{numbers of (j,k):j