General Bahr-Esseen inequalities and their applications.

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.

Erratum to: General Bahr-Esseen inequalities and their applications.

[This corrects the article DOI: 10.1186/s13660-017-1468-y.].