A nonstandard proof of de Finetti's theorem

Irfan Alam

Published 2019-12-05Version 1

We give a nonstandard analytic proof of de Finetti's theorem for an exchangeable sequence of Bernoulli random variables. The theorem postulates that such a sequence is conditionally independent given the value of a uniquely distributed random parameter on the interval $[0,1]$. We use combinatorial arguments to show that this probability distribution is induced by a hyperfinite sample mean.