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A Very General De Finetti-Type Theorem

In: Probability and Bayesian Statistics

Author

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  • Paul Ressel

    (Katholische Universität Eichstätt, Math.-Geogr. Fakultät)

Abstract

A few years ago it turned out that De Finetti’s famous theorem concerning exchangeable 0–1 valued random variables can also be proved by harmonic analysis means, applied to the special semigroup {(k,n) ∊ IN o 2 |k ≦ n}. This is no pure coincidence; a careful inspection of the new proof revealed that many other De Finetti-type theorems, old and new ones, could be shown the same way, among them Schoenberg’s representation of spherically symmetric random sequences, Hewitt and Savage’s far-reaching generalisation of De Finetti’s original result, and numerous characterisations of mixtures of i.i.d.-sequences with concrete prescribed distributions.

Suggested Citation

  • Paul Ressel, 1987. "A Very General De Finetti-Type Theorem," Springer Books, in: R. Viertl (ed.), Probability and Bayesian Statistics, pages 403-413, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-1885-9_41
    DOI: 10.1007/978-1-4613-1885-9_41
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