Slow convergence of Birkhoff ergodic averages

Let ᶻ\ be an ergodic action of the group Zⁿ by automorphisms of the probability space $(X,m)$, ∑ᵢ^∞ aᵢ<∞, aᵢ>0. For any sequence Mₖ→ +∞ there exist Nₖ>Mₖ and a function f∈ L₁(X,m) such that m(\ x:\ |\, A(x,Nₖ,f) - ∫ f \, dm\, |\ >\ aₖ \ )\ →\ 1, where A(x,N,f) = 1 Nⁿ ∑z∈ QN f(Tᶻx), QN=\(z₁,,zₙ)\\, :\, 1≤ z₁,,zₙ≤ N\.