An elementary proof of de Finetti's Theorem

TL;DR

This paper provides an elementary, self-contained proof of de Finetti's Theorem, making the fundamental result on exchangeable sequences more accessible to a wider audience.

Contribution

It introduces a new, simplified proof of de Finetti's Theorem, enhancing understanding and accessibility for researchers and students.

Findings

Proof is elementary and self-contained

Clarifies the structure of exchangeable sequences

Broadens accessibility of de Finetti's Theorem

Abstract

A sequence of random variables is called exchangeable if the joint distribution of the sequence is unchanged by any permutation of the indices. De Finetti's theorem characterizes all $\{0,1\}$-valued exchangeable sequences as a "mixture" of sequences of independent random variables. We present an new, elementary proof of de Finetti's Theorem. The purpose of this paper is to make this theorem accessible to a broader community through an essentially self-contained proof.