La convergence presque sûre des moyennes ergodiques suivant certaines sous-suites d'entiers

Jean-Paul Thouvenot

Séminaire Bourbaki (1989-1990)

  • Volume: 32, page 133-153
  • ISSN: 0303-1179

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Thouvenot, Jean-Paul. "La convergence presque sûre des moyennes ergodiques suivant certaines sous-suites d'entiers." Séminaire Bourbaki 32 (1989-1990): 133-153. <http://eudml.org/doc/110121>.

@article{Thouvenot1989-1990,
author = {Thouvenot, Jean-Paul},
journal = {Séminaire Bourbaki},
keywords = {maximal ergodic theorem; pointwise ergodic theorem; Weyl exponential sums; polynomial sequences; dynamical system; sequence of prime numbers},
language = {fre},
pages = {133-153},
publisher = {Société Mathématique de France},
title = {La convergence presque sûre des moyennes ergodiques suivant certaines sous-suites d'entiers},
url = {http://eudml.org/doc/110121},
volume = {32},
year = {1989-1990},
}

TY - JOUR
AU - Thouvenot, Jean-Paul
TI - La convergence presque sûre des moyennes ergodiques suivant certaines sous-suites d'entiers
JO - Séminaire Bourbaki
PY - 1989-1990
PB - Société Mathématique de France
VL - 32
SP - 133
EP - 153
LA - fre
KW - maximal ergodic theorem; pointwise ergodic theorem; Weyl exponential sums; polynomial sequences; dynamical system; sequence of prime numbers
UR - http://eudml.org/doc/110121
ER -

References

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  8. [B6] J. Bourgain - Pointwise ergodic theorems on arithmetic sets, with an appendix on return time sequences (jointly with H. Furstenberg, Y. Katznelson, D. Ornstein), Publications Mathématiques de l'I.H.E.S. n° 69, 1989, 5-45. Zbl0705.28008MR1019960
  9. [B7] J. Bourgain - Double recurrence and almost sure convergence, preprint, 1988. MR1037434
  10. [C] R.P. Calderon - Ergodic theory and translation invariant operators, Proc. Nat. Acad. Sci. U.S.A.59, 1968, 349-353. Zbl0185.21806MR227354
  11. [B-K] A. Brunel and M. Keane - Ergodic theorems for operator sequences, Z.F.W.12 , 1969, 231-240. Zbl0187.00904MR268934
  12. [F1] H. Furstenberg - Recurrence in ergodic theory and combinatorial number theory, Princeton U.P., 1981. Zbl0459.28023MR603625
  13. [F2] H. Furstenberg - Proceedings of the Durham Conference, June 1982. 
  14. [Lep] D. Lépingle - La variation d'ordre p des semi-martingales, Z.F.W.36, 1976, 295-316. Zbl0325.60047MR420837
  15. [Les] E. Lesigne - Sur la convergence ponctuelle de certaines moyennes ergodiques, C.R.A.S., Paris, t. 298, série I (1984). Zbl0579.60024MR765266
  16. [V] R.C. Vaughan - The Hardy-Littlewood circle method, Cambridge University Press, 1981. Zbl0455.10034MR628618
  17. [W] M. Wierdl - Pointwise ergodic theorem along the prime numbers, Israel Journal of Mathematics, Vol. 64, n° 3, 1988, 315-336. Zbl0695.28007MR995574

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