The return time theorem fails on infinite measure-preserving systems

Michael T. Lacey

Annales de l'I.H.P. Probabilités et statistiques (1997)

  • Volume: 33, Issue: 4, page 491-495
  • ISSN: 0246-0203

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Lacey, Michael T.. "The return time theorem fails on infinite measure-preserving systems." Annales de l'I.H.P. Probabilités et statistiques 33.4 (1997): 491-495. <http://eudml.org/doc/77579>.

@article{Lacey1997,
author = {Lacey, Michael T.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {ergodic measure-preserving system; sigma-finite measure-preserving system; aperiodic measure-preserving system},
language = {eng},
number = {4},
pages = {491-495},
publisher = {Gauthier-Villars},
title = {The return time theorem fails on infinite measure-preserving systems},
url = {http://eudml.org/doc/77579},
volume = {33},
year = {1997},
}

TY - JOUR
AU - Lacey, Michael T.
TI - The return time theorem fails on infinite measure-preserving systems
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1997
PB - Gauthier-Villars
VL - 33
IS - 4
SP - 491
EP - 495
LA - eng
KW - ergodic measure-preserving system; sigma-finite measure-preserving system; aperiodic measure-preserving system
UR - http://eudml.org/doc/77579
ER -

References

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  1. [AD] J. Aaronson and M. Denker, On the FLIL for certain ψ-mixing processes and infinite measure-preserving transformations, (English. French summary), C. R. Acad. Sci. Paris, Série I, Math., Vol. 313, 1991, pp. 471-475. Zbl0734.60033MR1127942
  2. [BL] A. Bellow and V. Losert, The weighted pointwise ergodic theorem and the individual ergodic theorem along subsequences, Trans. Amer. Math. Soc., Vol. 288, 1985, pp. 307-345. Zbl0619.47004MR773063
  3. [B] J. Bourgain, Almost sure convergence and bounded entropy, Israel J. Math., Vol. 63, 1988, pp. 79-97. Zbl0677.60042MR959049
  4. [BFKO] J. Bourgain, H. Furstenberg, Y. Katznelson and D. Ornstein, Return times of dynamical systems, Appendix to : Pointwise ergodic theorems for arithmetic sets, by J. Bourgain, Pub. Math. I.H.E.S., Vol. 69, 1989, pp. 5-45. Zbl0705.28008MR1019960
  5. [D] R.M. Dudley, Real Analysis and Probability, Wadsworth & Brooks/Cole, Pacific Grove, Gal., 1989. Zbl0686.60001
  6. [LPRW] M. Lacey, K. Petersen, D. Rudolph and M. Wierdl, Random ergodic theorems with universally representative sequences, Ann. Instit. H. Poincaré, Vol. 30, 1994, pp. 353-395. Zbl0813.28004MR1288356
  7. [W] M. Wichura, Functional law of the iterated logarithm for the partial sums of i.i.d. random variables in the domain of attraction of a completely asymmetric stable law, Ann. Probab., Vol. 2, 1974, pp. 1108-1138. Zbl0325.60029MR358950
  8. [WW] N. Wiener and A. Wintner, Harmonic analysis and ergodic theory, Amer. J. Math., Vol. 63, 1941, pp. 415-426. Zbl0025.06504MR4098

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