... n, for all n ≥ n0. Wedenote Wn⊂ Σna cover of minimal cardinality of F by n-cylinders. GivenN ∈ N, n ≤ N and τ ∈ [0, 1], we denote ΣN(Wn, τ ) the set of N-cylinders[α0, . . . , αN−1] ... θk.Proof. Given an (h, (1−θ), n)-cover of Σ, denoted W , we de ne Wk⊂ Σknas the set of kn-cylinders [α0, . . . , αkn−1] such that [αjn, . . . , α(j+1)n−1] ∈ W forall j ∈ [0, k−1], and ... be a subset of Σn, the set of n-cylinders in Σ;we denote Wc⊂ Σnits complement. For a given h > 0 and θ ∈ [0, 1], we saythat W is an (h, (1 − θ), n)-cover of Σ ifC∈WcˆChOph(χ)ψhL2(M)≤...