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Convergence-of-types theorem for simply connected nilpotent lie groups

Part of the Lecture Notes in Mathematics book series (LNM,volume 1379)

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  • Vector Space
  • Invariance Group
  • Proper Subspace
  • Convolution Semigroup
  • Lecture Note Math

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References

  1. Baldi, P.: Lois stables sur les deplacements de ℝd. In: Probability measures on groups. Proceedings Oberwolfach (1978). Lecture Notes in Math. 706, 1–9. Springer (1979).

    CrossRef  MathSciNet  Google Scholar 

  2. Billingsley, P.: Convergence of types in k-spaces. Z. Wahrscheinlichkeitstheorie verw. Geb. 5, 175–179 (1966).

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Drisch, T., Gallardo, L.: Stable laws on the Heisenberg group. In: Probability measures on groups. Proceedings Oberwolfach (1983). Lecture Notes Math. 1064, 56–79 (1984).

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Drisch, T., Gallardo, L.: Stable laws on the diamond group. Unpublished manuscript.

    Google Scholar 

  5. Feller, W.: An Introduction to Probability Theory and its Applications Vol. II. New York: Wiley (1966).

    MATH  Google Scholar 

  6. Fisz, M.: A generalization of a theorem of Khintchin. Studia Math. 14, 310–313 (1954).

    MathSciNet  MATH  Google Scholar 

  7. Gnedenko, B.W., Kolmogorov, A.N.: Limit distributions for sums of independent random variables. Cambridge: Addison-Wesley (1954).

    MATH  Google Scholar 

  8. Hazod, W.: Stable probability measures on groups and on vector spaces. A survey. In: Probability measures on groups VIII. Proceedings, Oberwolfach (1985). Lecture Notes Math. 1210, 304–352 (1986).

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Hazod, W., Siebert, E.: Continuous automorphism groups on a locally compact group contracting modulo a compact subgroup and applications to stable convolution semigroups. Semigroup Forum 33, 111–143 (1986).

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Hazod, W., Siebert, E.: Automorphisms on a Lie group contracting modulo a compact subgroup and applications to semistable convolution semigroups. J. of Theoretical Probability 1, 211–226 (1988).

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Hochschild, G.: The structure of Lie groups. San Francisco-London-Amsterdam: Holden Day Inc. (1965).

    MATH  Google Scholar 

  12. Jajte, R.: Semistable probability measures on ℝN. Studia Math. 61, 29–39 (1977).

    MathSciNet  MATH  Google Scholar 

  13. Jurek, Z.J.: Convergence of types, self-decomposability and stability of measures on linear spaces. In: Probability in Banach Spaces III. Proceedings Medford (1980). Lecture Notes Math. 860, 257–267 (1981).

    CrossRef  MathSciNet  Google Scholar 

  14. Letta, G.: Eine Bemerkung zum Konvergenzsatz für Verteilungstypen. Z. Wahrscheinlichkeitstheorie verw. Geb. 2, 310–313 (1964).

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Linde, W., Siegel, G.: On the convergence of types for Radon probability measures in Banach spaces. Probability on Banach Spaces. Sønderborg. Proceedings. Lecture Notes Math.

    Google Scholar 

  16. McCrudden, M.: On the Supports of Absolutely Continuous Gauss Measures on Connected Lie Groups. Mh. Math. 98, 295–310 (1984).

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Nobel, S.: Ph. D. Thesis University Dortmund. In preparation.

    Google Scholar 

  18. Sharpe, M.: Operator stable probability measures on vector groups. Trans. Amer. Math. Soc. 136, 51–65 (1969).

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. Urbanik, K.: Lévy's probability measures on Euclidean spaces. Studia Math. 44, 119–148 (1972).

    MathSciNet  MATH  Google Scholar 

  20. Urbanik, K.: Lévy's probability measures on Banach spaces. Studia Math. 63, 238–308 (1978).

    MathSciNet  MATH  Google Scholar 

  21. Weissmann, I.: On Convergence of Types and Processes in Euclidean Spaces. Z. Wahrscheinlichkeitstheorie verw. Geb. 37, 35–41 (1976).

    CrossRef  Google Scholar 

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© 1989 Springer-Verlag

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Hazod, W., Nobel, S. (1989). Convergence-of-types theorem for simply connected nilpotent lie groups. In: Heyer, H. (eds) Probability Measures on Groups IX. Lecture Notes in Mathematics, vol 1379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087848

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  • DOI: https://doi.org/10.1007/BFb0087848

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  • Print ISBN: 978-3-540-51401-5

  • Online ISBN: 978-3-540-46206-4

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