Notes on the projective limit theorem of Kolmogorov

  • Heinz KönigEmail author


The new systematization in measure and integration due to the author produced a version of the Kolmogorov projective limit theorem which is far more comprehensive than the previous ones. The present article is devoted to several consequences. In particular one obtains a topological version which applies to arbitrary Hausdorff spaces.


Inner premeasures Sequential and nonsequential ones Consistent families Projective limits 


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  1. 1.
    Bauer, H.: Wahrscheinlichkeitstheorie. 4th edn. de Gruyter (1991) (English translation 1996)Google Scholar
  2. 2.
    Bogachev, V.I.: Measure Theory, vol. I–II. Springer, Berlin (2007)Google Scholar
  3. 3.
    Kallenberg, O.: Foundation of Modern Probability, 2nd edn. Springer, Berlin (2002)CrossRefGoogle Scholar
  4. 4.
    Klenke, A.: Wahrscheinlichkeitstheorie, 2nd edn. Springer, Berlin (2008)zbMATHGoogle Scholar
  5. 5.
    Kolmogorov (=ff), A.: Grundbegriffe derWahrscheinlichkeitsrechnung. Springer (1933) (reprint 1973)Google Scholar
  6. 6.
    König, H.: Measure and Integration: An Advanced Course in Basic Procedures and Applications. Springer (1997) (corr. reprint 2009)Google Scholar
  7. 7.
    König, H.: The product theory for inner premeasures. Note Mat. 17, 235–249 (1997)MathSciNetzbMATHGoogle Scholar
  8. 8.
    König, H.: Measure and integration: an attempt at unified systematization. Rend. Istit. Mat. Univ. Trieste 34, 155–214 (2002). (Preprint no. 42 under
  9. 9.
    König, H.: Projective limits via inner premeasures and the true Wiener measure. Mediterr. J. Math. 1, 3–42 (2004)MathSciNetCrossRefGoogle Scholar
  10. 10.
    König, H.: Stochastic processes in terms of inner premeasures. Note Mat. 25(2), 1–30 (2005/2006)MathSciNetzbMATHGoogle Scholar
  11. 11.
    König, H.: The new maximal measures for stochastic processes. J. Anal. Appl. 26(1), 111–132 (2007)MathSciNetzbMATHGoogle Scholar
  12. 12.
    König, H.: Stochastic processes on the basis of new measure theory. In: Proc.Conf. Positivity IV—Theory and Applications, TU Dresden 25–29 July 2005, pp. 79–92. (Preprint (with corrections) No. 107 under
  13. 13.
    König, H.: Measure and Integral: New foundations after one hundred years. In: Functional Analysis and Evolution Equations (The Günter Lumer Volume). Birkhäuser 2007, pp. 405–422. (Preprint (with mreformulations) No. 175 under
  14. 14.
    König, H.: Measure and Integration: The basic extension theorems. (Preprint No. 230 under
  15. 15.
    Marczewski, E.: On compact measures. Fund. Math. 40, 113–124 (1953)MathSciNetGoogle Scholar
  16. 16.
    Rao, M.M.: Measure Theory and Integration, 2nd edn. Marcel Dekker, New York (2004)zbMATHGoogle Scholar

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© Springer Basel 2012

Authors and Affiliations

  1. 1.Fakultät für Mathematik und InformatikUniversität des SaarlandesSaarbrückenGermany

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