The Annals of Probability

A Continuous Version of De Finetti's Theorem

L. Accardi and Y. G. Lu

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A continuous version of De Finetti's theorem is proved in which the role of the homogeneous product states is played by the independent increment stationary processes on the real line. The proof is based on a conditional, finite De Finetti's theorem (i.e., a result involving only a finite number of random variables and exchangeable conditional expectations rather than exchangeable probabilities). Our technique of proof improves and simplifies a result of Freedman and includes a generalization of the quantum De Finetti's theorem as well as some more recent variants of it. The last section of the paper is an attempt to answer a question of Diaconis and Freedman.

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Ann. Probab., Volume 21, Number 3 (1993), 1478-1493.

First available in Project Euclid: 19 April 2007

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Primary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization
Secondary: 60C05: Combinatorial probability

De Finetti's theorem exchangeable increments conditional finite De Finetti's theorem exchangeable conditional expectations


Accardi, L.; Lu, Y. G. A Continuous Version of De Finetti's Theorem. Ann. Probab. 21 (1993), no. 3, 1478--1493. doi:10.1214/aop/1176989127.

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