A Characterization of a New Type of Strong Law of Large Numbers

TL;DR

This paper introduces a new characterization of a strong law of large numbers for i.i.d. real-valued variables, extending to Banach spaces, based on advanced inequalities and techniques.

Contribution

It provides a novel type of strong law of large numbers and extends the results to Banach space settings using recent inequalities.

Findings

New strong law of large numbers characterized

Extensions to Banach space setting provided

Utilizes advanced inequalities for proofs

Abstract

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.