Geodesic
Weighted Means, Strict Ergodicity, and Uniform Distributions
Matematičeskie zametki, Tome 78 (2005) no. 3, pp. 358-367

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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. 
@article{MZM_2005_78_3_a3,
     author = {V. V. Kozlov},
     title = {Weighted {Means,} {Strict} {Ergodicity,} and {Uniform} {Distributions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {358--367},
     publisher = {mathdoc},
     volume = {78},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_3_a3/}
}
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V. V. Kozlov. Weighted Means, Strict Ergodicity, and Uniform Distributions. Matematičeskie zametki, Tome 78 (2005) no. 3, pp. 358-367. http://geodesic.mathdoc.fr/item/MZM_2005_78_3_a3/