manuscripta mathematica

, Volume 24, Issue 2, pp 179–190 | Cite as

Two theorems on poisson measures on a topological group

  • Eberhard Siebert


Our first theorem is concerned with the convergence of nets of Poisson measures on a topological group. As a corollary we obtain a characterization of Poisson measures. The second theorem gives a characterization of elementary Poisson measures.


Number Theory Algebraic Geometry Topological Group Poisson Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    BADRIKIAN,A.: Séminaire sur les fonctions aléatoires linéaires et les mesures cylindriques. Lecture Notes in Mathematics 139. Berlin-Heidelberg-New York: Springer 1970.Google Scholar
  2. 2.
    BOURBAKI,N.: Eléments des Mathématique. Livre VI Intégration, chapitre IX. Paris: Hermann 1969.Google Scholar
  3. 3.
    HAZOD,W.: Einige Sätze über unendlich teilbare Wahrscheinlichkeitsmaße auf lokalkompakten Gruppen. Arch. Math. 16, 297–312 (1975).Google Scholar
  4. 4.
    PARTHASARATHY,K.R.: Probability measures on metric spaces. New York-London: Academic Press 1967.Google Scholar
  5. 5.
    SCHMETTERER,L.: On Poisson laws and related questions. Proc. 6th Berkeley Symp. Vol. II, 169–185 (1972).Google Scholar
  6. 6.
    SIEBERT, E.: Wahrscheinlichkeitsmaße auf lokalkompakten maximal fastperiodischen Gruppen. Dissertation, Tübingen 1972 (unpublished).Google Scholar
  7. 7.
    SIEBERT,E.: Convergence and convolutions of probability measures on a topological group. Ann. of Prob. 4, 433–443 (1976).Google Scholar
  8. 8.
    SIEBERT,E.: Fourier analysis and limit theorems for convolution semigroups on a locally compact group. Preprint (1977). To appear.Google Scholar
  9. 9.
    URBANIK, K.: Poisson-Distributions on compact Abelian topological groups. Coll. Math. 6, 13–24 (1958).Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Eberhard Siebert
    • 1
  1. 1.Mathematisches Institut der UniversitätTübingenBundesrepublik Deutschland

Personalised recommendations