A lacunary sequence is an increasing integer sequence θ={kr} such that kr−kr−1→∞ as
r→∞. A sequence x is called sθ-convergent to
L provided that for each ϵ>0, limr(1/(kr−kr−1)){the number of kr−1<k≤kr:|xk−L|≥ϵ}=0. In this paper, we study the
general description of inclusion between two arbitrary lacunary
sequences convergent.