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 θr,s={(kr,ls)}θr,s={(kr,ls)} be a double lacunary sequence; the two nonnegative sequences x=(xk,l)x=(xk,l) and y=(yk,l)y=(yk,l) are said to be asymptotically double lacunary statistically equivalent of multiple LL provided that for every ε>0ε>0P−limr,s1hr,s|{(k,l)∈Ir,s:|xk,lyk,l−L|≥ε}|=0(denoted by x∽Sθr,sLy) and simply asymptotically double lacunary statistically equivalent if L=1L=1.