Israel Journal of Mathematics

, Volume 61, Issue 1, pp 73–84

On the pointwise ergodic theorem onLp for arithmetic sets

  • J. Bourgain


The purpose of this note is to show how the results of [B] on the pointwise ergodic theorem forL2-functions may be extended toLp for certainp<2. More precisely, we give a proof of the almost sure convergence of the means\(\frac{1}{N}\sum\limits_{1\underline \le n\underline \le N} {T^{(n1)} } \) (t≧1) given a dynamical system (Ω,B, μ, T) andf of classLp(Ω,μ),p>(√5+1)/2.


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Copyright information

© The Weizmann Science Press of Israel 1988

Authors and Affiliations

  • J. Bourgain
    • 1
  1. 1.IHESBures-sur-YvetteFrance

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