Kozlov, V. V. Weighted averages, uniform distribution, and strict ergodicity. (English) Zbl 1145.11057 Russ. Math. Surv. 60, No. 6, 1121-1146 (2005); translation from Usp. Mat. Nauk 60, No. 6, 115-138 (2005). The article gives an overview of various generalizations of the classical concept of uniform distribution. The first digit paradox (Benford’s law) is discussed and uniform distribution with respect to Riesz and Voronoi summation methods is considered. Using these generalizations of Cesàro summability ergodic theorems and variants of the strong law of large numbers and the iterated logarithm are given. The last chapter lists some open problems. Reviewer: Martin Blümlinger (Wien) Cited in 2 Documents MSC: 11K36 Well-distributed sequences and other variations 28D05 Measure-preserving transformations 60F15 Strong limit theorems Keywords:uniform distribution; Riesz convergence; Voronoi convergence; strict ergodicity; weighted averages; Strong law of large numbers; ergodic theorem; Benford’s law PDF BibTeX XML Cite \textit{V. V. Kozlov}, Russ. Math. Surv. 60, No. 6, 1121--1146 (2005; Zbl 1145.11057); translation from Usp. Mat. Nauk 60, No. 6, 115--138 (2005) Full Text: DOI OpenURL