An entropy theorem for computing the capacity of weakly(d,k)-constrained sequences

We find an analytic expression for the maximum of the normalized entropy -Σ_iϵTp_iln p_i/Σ_iϵTip_i where the set T is the disjoint union of sets S_n of positive integers that are assigned probabilities P_n, Σ_nP_n =1. This result is applied to the computation of the capacity of weakly (d,k)-constrained sequences that are allowed to violate the (d,k)-constraint with small probability