On the Law of Large Numbers for non-equally distributed weakly dependent random variables

TL;DR

This paper introduces three versions of the Weak Law of Large Numbers applicable to weakly dependent, non-identically distributed random variables with finite or infinite expectations, expanding classical probability theory.

Contribution

It proposes new versions of the Weak Law of Large Numbers for weakly dependent, non-identically distributed variables with possibly infinite expectations.

Findings

Three versions of the Weak Law are established.

Applicable to variables with finite or infinite expectations.

Extends classical results to weakly dependent, non-i.i.d. variables.

Abstract

Three versions of the Weak Law of Large Numbers are proposed for weakly dependent and generally speaking non-equally distributed random variables, with finite or possibly infinite expectations.