The Lyapunov condition, sometimes known as Lyapunov's central limit theorem, states that if the (2 + ϵ)th moment (with ϵ>0) exists for a statistical distribution of independent random variates x_i (which need not necessarily be from same distribution), the means μ_i and variances σ_i^2 are finite, and r_n^(2 + ϵ) = sum_(i = 1)^n 〈( left bracketing bar x_i - μ_i right bracketing bar )^(2 + ϵ) 〉, then if lim_(n->∞) r_n/s_n = 0, where s_n^2 = sum_(i = 1)^n σ_i^2, the central limit theorem holds.