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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Strong uniform distributions and ergodic theorems


Authors: J. R. Blum and L.-S. Hahn
Journal: Proc. Amer. Math. Soc. 47 (1975), 378-382
DOI: https://doi.org/10.1090/S0002-9939-1975-0361000-9
MathSciNet review: 0361000
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Abstract | References | Additional Information

Abstract: Let $ G$ and $ H$ be locally compact $ \sigma $-compact abelian groups, $ \mathcal{A}$ a mapping from $ G$ to $ H$, and $ \{ {\mu _n}\} _{n = 1}^\infty $ a sequence of measures on $ G$. We define the notions: `` $ \mathcal{A}$ is a uniform distribution with respect ot $ \{ {\mu _n}\} $'' and `` $ \mathcal{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.


References [Enhancements On Off] (What's this?)

  • [1] J. R. Blum and B. Eisenberg, Generalized summing sequences and the mean ergodic theorem, Proc. Amer. Math. Soc. 42 (1974), 423-429. MR 0330412 (48:8749)
  • [2] E. Hewitt and K. Ross, Abstract harmonic analysis. Vol. I: Structure of topological groups. Integration theory, group representations, Die Grundlehren der math. Wissenschaften, Band 115, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #158. MR 551496 (81k:43001)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0361000-9
Article copyright: © Copyright 1975 American Mathematical Society

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