Skip to main content
Log in

A metric study involving independent sequences

  • Published:
Journal d’Analyse Mathématique Aims and scope

Abstract

We investigate the distribution of sequences in compact metric spaces, involving spectra of flows and notions of statistical independences. We pay attention to sequences closely related to group extensions of flows.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L. M. Abramov and V. A. Rohlin,Entropy of skew product of mappings with invariant measure (Russian), Vestnik Leningrad Univ.17, no 7 (1962), 5–13; Amer. Math. Soc. Transl. (Ser. 2)48 (1965), 255–265.

    MathSciNet  Google Scholar 

  2. R. L. Adler and P. C. Shields,Skew products of Bernoulli shift with rotations I, Israel J. Math.12 (1972), 215–222;II ibidem R. L. Adler and P. C. Shields,Skew products of Bernoulli shift with rotations I, Israel J. Math.19 (1974), 228–236.

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Coquet,Type de répartition complète des suites, Ann. Fac. Sci. Univ. Toulouse2 (1980), 137–155.

    MATH  MathSciNet  Google Scholar 

  4. J. Coquet, T. Kamae and M. Mendès-France,Sur la mesure spectrale de certaines suites arithmétiques, Bull. Soc. Math. Fr.105 (1977), 369–384.

    MATH  Google Scholar 

  5. J. Coquet and P. Liardet,Répartitions uniformes des suites et indépendance statistique, Compos. Math.51 (1984), 215–236.

    MATH  MathSciNet  Google Scholar 

  6. J. P. Cornfeld, S. V. Fomin and Ya. G. Sinai,Ergodic Theory, Springer-Verlag, Grundlehren der mathematischen Wissenschaften245.

  7. N. A. Friedman and D. S. Ornstein,On isomorphism of weak Bernoulli transformations, Advances in Math.5 (1971), 365–394.

    Article  MathSciNet  Google Scholar 

  8. H. Furstenberg,Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation, Math. Syst. Theory1 (1967), 1–49.

    Article  MATH  MathSciNet  Google Scholar 

  9. H. Furstenberg,Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton University Press.

  10. T. Kamae,Subsequences of normal sequences, Israel J. Math.16 (1973), 121–149.

    Article  MathSciNet  Google Scholar 

  11. T. Kamae,Nutural singularity of spectra of dynamical systems given by “sums of digits” to different bases, Société Math. France, Astérisque49 (1977), 109–114.

    MathSciNet  Google Scholar 

  12. L. Kuipers and H. Niederreiter,Uniform Distribution of Sequences, Wiley-Interscience, 1974.

  13. P. Liardet,Propriétés génériques de processus croisés, Israel J. Math.39 (1981), 303–325.

    Article  MATH  MathSciNet  Google Scholar 

  14. D. Ornstein,Ergodic Theory, Randomness and Dynamical Systems, Yale Math. Monographs no 5, Yale University, 1974.

  15. W. Parry,Ergodic properties of affine transformations and flows on nilmanifold, Amer. J. Math.91 (1969), 757–771.

    Article  MATH  MathSciNet  Google Scholar 

  16. G. Rauzy,Caractérisation des ensembles normaux, Bull. Soc. Math. Fr.98 (1970), 401–414.

    MATH  MathSciNet  Google Scholar 

  17. G. Rauzy,Propriétés statistiques de suites arithmétiques, P.U.F. Collection Sup. le Mathématicien15 (1976).

  18. D. J. Rudolph,Classifying the isometric extensions of a Bernoulli shift, J. Analyse Math.34 (1979), 36–60.

    Article  MathSciNet  Google Scholar 

  19. R. K. Thomas,Metric properties of transformations of G-spaces, Trans. Amer. Math. Soc.160 (1971), 103–117.

    Article  MATH  MathSciNet  Google Scholar 

  20. R. K. Thomas,The addition theorem for the entropy of transformations of G-spaces, Trans. Amer. Math. Soc.160 (1971), 119–130.

    Article  MATH  MathSciNet  Google Scholar 

  21. W. Veech,Minimal transformation groups with distal points, Bull. Amer. Math. Soc.75 (1968), 481–486.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Coquet, J., Liardet, P. A metric study involving independent sequences. J. Anal. Math. 49, 15–53 (1987). https://doi.org/10.1007/BF02792891

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02792891

Keywords

Navigation