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