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This paper proves the Baum--Katz theorem for sequences of pairwiseindependent identically distributed random variables with general normingconstants under optimal moment conditions. The proof exploits some propertiesof slowly varying functions and the de Bruijn conjugates, and uses thetechniques developed by Rio (1995) to avoid using the maximal typeinequalities.

On the Baum--Katz theorem for sequences of pairwise independent random variables with regularly varying normalizing constants