The author presents a simple and easily interpretable probabilistic formulation of the Lindeberg condition and demonstrates its sufficiency and partial necessity in the Central Limit Theorem (CTL) using elementary means. The proof is based on the so-called zero bias transformation, which is motivated by Stein’s characterization of the mean zero normal distribution with variance $σ^2$.

Reviewer:

Wiesław Dziubdziela (Kielce)