Given a sequence of independent random variates X_1, X_2, ..., if σ_k^2 = var(X_k) and ρ_n^2 congruent max_(k<=n)(σ_k^2/s_n^2), then lim_(n->∞) ρ_n^2 = 0. This means that if the Lindeberg condition holds for the sequence of variates X_1, ..., then the variance of an individual term in the sum S_n of X_k is asymptotically negligible. For such sequences, the Lindeberg condition is necessary as well as sufficient for the Lindeberg-Feller central limit theorem to hold.

Berry-Esséen theorem | central limit theorem | Lindeberg condition