A nonstandard proof of de Finetti's theorem
arXiv:1912.02784 · doi:10.31390/josa.1.4.15
Abstract
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 uniquely representable as a mixture of iid sequences of Bernoulli random variables. We use combinatorial arguments to show that this probability distribution is induced by a hyperfinite sample mean.
14 pages; added a brief introduction to nonstandard methods in the appendix, fixed minor errors/typos. arXiv admin note: text overlap with arXiv:1901.10507