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Extreme point method in probability theory

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Probability-Winter School

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 472))

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References

  1. N.H. Bingham, Factorization theory and domains of attration for generalized convolution algebras, Proceedinds of the London Math. Soc. 23 (1971), 16–30.

    Article  MathSciNet  MATH  Google Scholar 

  2. N. Bourbaki, Éléments de mathématique, I. Les structures fondamentales de l'analyse, Livre III, Topologie génerale, Paris 1951.

    Google Scholar 

  3. G. Choquet, Le théorème do représentation intégrale dans les ensembles convexes compacts, ANN. Inst. Fourier, Grenoble 10 (1960), 333–344.

    Article  MathSciNet  MATH  Google Scholar 

  4. E.B. Dynkin, Klassy ekvivalentnych slučainych veličin, Uspehi Mat. Nauk. 8, vol 54 (1953), 125–134.

    MathSciNet  Google Scholar 

  5. B. de Finetti, Funzione caratteristica di un fenomeno aleatorio, Atti della R. Accademia Nazionale dei Lincei, Ser. 6, Memorie, Classe di Scienze Fisiche, Matematiche e Naturali, 4 (1931), 251–299.

    MATH  Google Scholar 

  6. B. de Finetti, La prévision: ses lois logiques, ses sources subjectives, Ann. Inst. Henri Poincaré 7(1937), 1–68.

    MATH  Google Scholar 

  7. J. Haag, Sur un problème général do probabilités et ses diverses applications, Proceedings of the International Congress of Mathematicians, Toronto, 1924, 659–674.

    Google Scholar 

  8. E. Hewitt and L.J. Savage, Symmetric measures on cartesian products, Trans. Amer. Math. Soc. 80 (1955), 470–501.

    Article  MathSciNet  MATH  Google Scholar 

  9. S. Johansen, An application of extreme point methods to the representation of infinitely divisible distributions, Zeitschrift für Wahrscheinlichkeitstheorie und verw. Gebiete 5 (1966), 304–316.

    Article  MathSciNet  MATH  Google Scholar 

  10. D.G. Kendall, Extreme—point methods in stochastic analysis, Zeitschrift für Warscheinlichkeitstheorie und verw. Gebiete, 1 (1963), 295–300.

    Article  MathSciNet  Google Scholar 

  11. D.G. Kendall, On finite and infinite sequences of exchangeable events, Studia Scientiarum Math. Hung. 2 (1967), 319–327.

    MathSciNet  MATH  Google Scholar 

  12. A.Ya. Khinchine, O klassah ekvivalentnyh sobytiî, Doklady Akad. Nauk SSSR, 85 (1952), 713–714.

    MathSciNet  Google Scholar 

  13. A.Ya. Khinchine, Sur les classes d'événements équivalents, Mat. Sbornik 39 (1932), 40–43.

    MATH  Google Scholar 

  14. J.F. Kingman, Random walks with spherical symmetry, Colloquium on Combinatorical Methods in Probability Theory, Aarhus (1962), 40–46.

    Google Scholar 

  15. M.G. Krein and D.P. Milman, On extreme points of regularly convex sets, Studia Math. 9 (1940), 133–138.

    MathSciNet  MATH  Google Scholar 

  16. J. Kucharczak and K. Urhanik, Quasi-stable functions, Bull. Acad. Pol. Sci., Série des sci. math., astronom. et phys. 22 (1974), 263–268.

    MathSciNet  MATH  Google Scholar 

  17. P. Lévy, Théorie de l'addition des variables aléatoires, Paris 1954.

    Google Scholar 

  18. M. Loève, Probability theory, New York, 1950.

    Google Scholar 

  19. K. Numakura, On bicompact semigroups, Math. J. Okayama Univ. 1 (1952), 99–108.

    MathSciNet  MATH  Google Scholar 

  20. A. B. Paalman-de Miranda, Topological semigroups, Amsterdam 1964.

    Google Scholar 

  21. R.P. Phelps, Lectures on Choquet's theorem, Princeton 1966.

    Google Scholar 

  22. A. Rényi and P. Révész, A study of sequences of equivalent events as special stable sequences, Publ. Math. Debrecen, 10 (1963), 319–325.

    MathSciNet  MATH  Google Scholar 

  23. Cz. Ryll-Nardzewski, On stationary sequences of random variables and the de Finetti's equivalence, Coll. Math. 4 (1955), 149–156.

    MathSciNet  MATH  Google Scholar 

  24. M. Sharpe, Operator—stable probability distributions on vector groups, Trans. Amer. Math. Soc. 136 (1969), 51–65.

    Article  MathSciNet  MATH  Google Scholar 

  25. K. Urbanik, Generalized convolutions, Studia Math. 23 (1964), 217–245.

    MathSciNet  MATH  Google Scholar 

  26. K. Urbanik, Generalized convolutions II, Studia Math. 45 (1973), 57–70.

    MathSciNet  MATH  Google Scholar 

  27. K. Urbanik, A representation of self-decomposable distributions, Bull. Acad. Pol. Sci., Serie des sci. math., astronom. et phys. 16 (1968), 196–204.

    MathSciNet  MATH  Google Scholar 

  28. K. Urbanik, Lévy's probability measures on Euclidean spaces, Studia Math. 44 (1972), 119–148. *** DIRECT SUPPORT *** A00J4108 00005

    MathSciNet  MATH  Google Scholar 

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Z. Ciesielski K. Urbanik W. A. Woyczyński

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© 1975 Springer-Verlag

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Urbanik, K. (1975). Extreme point method in probability theory. In: Ciesielski, Z., Urbanik, K., Woyczyński, W.A. (eds) Probability-Winter School. Lecture Notes in Mathematics, vol 472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081953

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  • DOI: https://doi.org/10.1007/BFb0081953

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07190-7

  • Online ISBN: 978-3-540-37556-2

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