Strong uniform distributions and ergodic theorems
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- by J. R. Blum and L.-S. Hahn PDF
- Proc. Amer. Math. Soc. 47 (1975), 378-382 Request permission
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
- Julius Blum and Bennett Eisenberg, Generalized summing sequences and the mean ergodic theorem, Proc. Amer. Math. Soc. 42 (1974), 423–429. MR 330412, DOI 10.1090/S0002-9939-1974-0330412-0
- Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 378-382
- DOI: https://doi.org/10.1090/S0002-9939-1975-0361000-9
- MathSciNet review: 0361000