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A new proof of the Komlós-Révész-theorem
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  • Published: September 1990

A new proof of the Komlós-Révész-theorem

  • Rolf Trautner1 

Probability Theory and Related Fields volume 84, pages 281–287 (1990)Cite this article

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  • 6 Citations

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Summary

The Komlós-Révész theorem states: For r.v.s.X n with ‖X n ‖1≦M there exists a subsequenceX k n and a r.v.X with ‖X‖1≦M such that

$$\frac{{X_{k_1 } + \cdots + X_{k_n } }}{n}\xrightarrow{{a.s.}}X$$

. A new proof as given by using weak compactness inL 2, a theorem of Menchoff for a.s. convergence of subsequences of orthogonal series and the standard truncation technique of the strong law.

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References

  1. Aldous, D.J.: Limit theorems for subsequences of arbitrarily-dependent sequences of random variables. Z. Wahrscheinlichkeitstheor. Verw. Geb.40, 59–82 (1977)

    Google Scholar 

  2. Alexits, G.: Konvergenzprobleme der Orthogonalreihen. Berlin: Deutscher Verlag der Wissenschaften 1960

    Google Scholar 

  3. Berkes, I.: The law of the iterated logarithm for subsequences of random variables. Z. Wahrscheinlichkeitstheor. Verw. Geb.30, 209–215 (1974)

    Google Scholar 

  4. Chatterji, S.D.: A subsequence principle in probability theory. Bull. Am. Math. Soc.80, 495–497 (1974)

    Google Scholar 

  5. Chatterji, S.D.: A principle of subsequences in probability theory. Adv. Math.13, 31–54 (1974)

    Google Scholar 

  6. Gaposhkin, V.F.: Convergence and limit theorems for sequences of random variables. Theor. Probab. Appl.17, 379–399 (1972)

    Google Scholar 

  7. Komlós, J.: A generalization of a problem of Steinhaus. Acta Math. Acad. Sci. Hung.18, 217–279 (1967)

    Google Scholar 

  8. Révész, P.: On a problem of Steinhaus. Acta Math. Acad.Sci. Hung.16, 311–318 (1965)

    Google Scholar 

  9. Stadtmüller, U., Trautner, R.: Ratio tauberian theorems for Laplace transforms without monotonicity assumptions. Quart. J. Math., Oxford (2)36, 363–381 (1985)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Abteilung für Stochastik, Universitat Ulm, Oberer Eselsberg, D-7900, Ulm, Federal Republic of Germany

    Rolf Trautner

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  1. Rolf Trautner
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Cite this article

Trautner, R. A new proof of the Komlós-Révész-theorem. Probab. Th. Rel. Fields 84, 281–287 (1990). https://doi.org/10.1007/BF01197885

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  • Received: 11 April 1988

  • Revised: 11 April 1989

  • Issue Date: September 1990

  • DOI: https://doi.org/10.1007/BF01197885

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Theorem State
  • Weak Compactness
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