Strong Uniform Distributions and Ergodic Theorems

Let G and H be locally compact σ-compact abelian groups, a a mapping from G to H, and {μn}∞ n = 1a sequence of measures on G. We define the notions: "a is a uniform distribution with respect to {μn}" and "a is a strong uniform distribution". We give a number of examples of these...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1975-02, Vol.47 (2), p.378-382
Main Authors: Blum, J. R., L.-S. Hahn
Format: Article
Language:English
Subjects:
Ergodic theory
Haar measures
Homomorphisms
Integers
Mathematical functions
Mathematical sequences
Mathematical theorems
Perceptron convergence procedure
Topological theorems
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Summary:Let G and H be locally compact σ-compact abelian groups, a a mapping from G to H, and {μn}∞ n = 1a sequence of measures on G. We define the notions: "a is a uniform distribution with respect to {μn}" and "a is a strong uniform distribution". We give a number of examples of these notions and derive some general individual ergodic theorems for measure-preserving transformations with discrete spectrum.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-1975-0361000-9