Hostname: page-component-6766d58669-76mfw Total loading time: 0 Render date: 2026-05-24T09:46:25.536Z Has data issue: false hasContentIssue false
  • English
  • Français

Quantitative ergodic theorems for weakly integrable functions

Published online by Cambridge University Press:  29 November 2012

ALAN HAYNES
ALAN HAYNES*
Affiliation:
School of Mathematics, University of Bristol, Bristol, UK (email: alan.haynes@bristol.ac.uk)
Get access Rights & Permissions [Opens in a new window]

Abstract

Under suitable hypotheses we establish a quantitative pointwise ergodic theorem which applies to trimmed Birkhoff sums of weakly integrable functions.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 2 , April 2014 , pp. 534 - 542
Copyright
©2012 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1]Aaronson, J.. On the ergodic theory of non-integrable functions and infinite measure spaces. Israel J. Math. 27(2) (1977), 163–173.Google Scholar
[2]Aaronson, J. and Nakada, H.. Trimmed sums for non-negative, mixing stationary processes. Stochastic Process. Appl. 104(2) (2003), 173–192.Google Scholar
[3]Aaronson, J. and Nakada, H.. On the mixing coefficients of piecewise monotonic maps. Israel J. Math. 148 (2005), 1–10.Google Scholar
[4]Avigad, J.. The metamathematics of ergodic theory. Ann. Pure Appl. Logic 157(2–3) (2009), 64–76.Google Scholar
[5]Avigad, J., Gerhardy, P. and Towsner, H.. Local stability of ergodic averages. Trans. Amer. Math. Soc. 362(1) (2010), 261–288.Google Scholar
[6]Diamond, H. G. and Vaaler, J. D.. Estimates for partial sums of continued fraction partial quotients. Pacific J. Math. 122(1) (1986), 73–82.Google Scholar
[7]Kachurovskii, A. G.. Rates of convergence in ergodic theorems. Uspekhi Mat. Nauk 51(4(310)) (1996), 73–124, Engl. transl. Russian Math. Surveys 51(4) (1996) 653–703.Google Scholar
[8]Mori, T.. The strong law of large numbers when extreme terms are excluded from sums. Z. Wahrscheinlichkeitstheor. Verw. Geb. 36(3) (1976), 189–194.Google Scholar
[9]Mori, T.. Stability for sums of i.i.d. random variables when extreme terms are excluded. Z. Wahrscheinlichkeitstheor. Verw. Geb. 40(2) (1977), 159–167.Google Scholar
[10]Nakada, H. and Natsui, R.. Some metric properties of α-continued fractions. J. Number Theory 97 (2002), 287–300.Google Scholar
[11]Nakada, H. and Natsui, R.. On the metrical theory of continued fraction mixing fibred systems and its application to Jacobi–Perron algorithm. Monatsh. Math. 138(4) (2003), 267–288.CrossRefGoogle Scholar
[12]Philipp, W.. A conjecture of Erdos on continued fractions. Acta Arith. 28(4) (1975/76), 379–386.Google Scholar
[13]Walters, P.. An Introduction to Ergodic Theory (Graduate Texts in Mathematics, 79). Springer, New York, 1982.Google Scholar