Permutation invariant strong law of large numbers for exchangeable sequences

TL;DR

This paper establishes a permutation invariant strong law of large numbers specifically for exchangeable sequences, combining classical theorems to extend the law's applicability.

Contribution

It introduces a permutation invariant version of the strong law of large numbers for exchangeable sequences, integrating multiple foundational theorems.

Findings

Permutation invariance in the strong law established.

Extension of classical results to exchangeable sequences.

Proof combines Komlós-Berkes, classical SLLN, and de Finetti's theorem.

Abstract

We provide a permutation invariant version of the strong law of large numbers for exchangeable sequences of random variables. The proof consists of a combination of the Koml\'{o}s-Berkes theorem, the usual strong law of large numbers for exchangeable sequences and de Finetti's theorem.