We study the Bahr-Esseen inequality. We show that the Bahr-Esseen inequality holds with exponent p if it holds with exponent [Formula: see text] for the truncated and centered random variables. The Bahr-Esseen inequality is also true if the truncated random variables are acceptable. We then apply the results to obtain weak and strong laws of large numbers and complete convergence.
Keywords: Bahr-Esseen inequality; Rosenthal inequality; acceptable random variables; complete convergence; exponential inequality; rate of convergence; strong law of large numbers; weakly orthant-dependent sequences.