We study the Bahr-Esseen inequality. We show that the Bahr-Esseen inequality holds
with exponent p if it holds with exponent q > p 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.

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• General Bahr-Esseen inequalities and their applications