On asymptotically double lacunary statistically equivalent sequences

This work presents the following definition which is a natural combination of the definition for asymptotically equivalent, double statistically limited and double lacunary sequences. Let θ r , s = { ( k r , l s ) } be a double lacunary sequence; the two nonnegative sequences x = ( x k , l ) and y = ( y k , l ) are said to be asymptotically double lacunary statistically equivalent of multiple L provided that for every ε > 0 P − lim r , s 1 h r , s | { ( k , l ) ∈ I r , s : | x k , l y k , l − L | ≥ ε } | = 0 ( denoted by  x ∽ S θ r , s L y ) and simply asymptotically double lacunary statistically equivalent if L = 1 .