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By applying results obtained from the new versions of the classical Levy, Ottaviani, and Hoffmann-Jorgensen (1974) inequalities proved by Li and Rosalsky(2013) and by using techniques developed by Hechner and Heinkel (2010), we provide a characterization of a new type of strong law of large numbers for independent and identically distributed real-valued random variables. Versions of this strong law of large numbers are also presented in a Banach space setting.

A characterization of a new type of strong law of large numbers