# On the Strong Law of Large Numbers for Sequences of Pairwise Independent Random Variables

## TL;DR

This paper extends the strong law of large numbers to sequences of pairwise independent, non-identically distributed random variables, providing new conditions and generalizations, including results with arbitrary norming sequences.

## Contribution

It introduces new sufficient conditions for the SLLN to hold for pairwise independent variables, generalizing previous results and allowing for arbitrary norming sequences.

## Key findings

- Established new SLLN conditions for pairwise independent variables
- Generalized Etemadi's extension of Kolmogorov's SLLN
- Some results hold with arbitrary norming sequences

## Abstract

We establish new sufficient conditions for the applicability of the strong law of large numbers (SLLN) for sequences of pairwise independent non-identically distributed random variables. These results generalize Etemadi's extension of Kolmogorov's SLLN for identically distributed random variables. Some of the obtained results hold with an arbitrary norming sequence in place of the classical normalization.