Mathematical Notes

, Volume 78, Issue 3–4, pp 329–337 | Cite as

Weighted Means, Strict Ergodicity, and Uniform Distributions

  • V. V. Kozlov
Article

Abstract

We strengthen the well-known Oxtoby theorem for strictly ergodic transformations by replacing the standard Cesaro convergence by the weaker Riesz or Voronoi convergence with monotonically increasing or decreasing weight coefficients. This general result allows, in particular, to strengthen the classical Weyl theorem on the uniform distribution of fractional parts of polynomials with irrational coefficients.

Key words

Weyl theorem Cesaro and Voronoi convergences Borel measure Oxtoby's theorem strictly ergodic transformation Riesz summation method 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • V. V. Kozlov
    • 1
  1. 1.V. A. Steklov Mathematics InstituteRussian Academy of SciencesMoscowRussia

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