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Arithmetic averages of rotations of measurable functions

Published online by Cambridge University Press:  14 October 2010

Zoltán Buczolich
Zoltán Buczolich
Affiliation:
Department of Analysis, Eötvös University, Budapest, Múzeum krt. 6-8, H-1088, Hungary
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Abstract

We give examples of non-integrable measurable functions for which there are ‘many’ rotations such that the arithmetic (ergodic) averages exist for almost every x. We also show that if the above ergodic averages exist for almost every x for a set of rotations of positive measure, then the function should be integrable on [0, 1].

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 6 , December 1996 , pp. 1185 - 1196
Copyright
Copyright © Cambridge University Press 1996

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References

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