an:05268250
Zbl 1145.11057
Kozlov, V. V.
Weighted averages, uniform distribution, and strict ergodicity
EN
Russ. Math. Surv. 60, No. 6, 1121-1146 (2005); translation from Usp. Mat. Nauk 60, No. 6, 115-138 (2005).
00125437
2005
j
11K36 28D05 60F15
uniform distribution; Riesz convergence; Voronoi convergence; strict ergodicity; weighted averages; Strong law of large numbers; ergodic theorem; Benford's law
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 Ces??ro 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.
Martin Bl??mlinger (Wien)