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Arithmetic averages of rotations of measurable functions
Published online by Cambridge University Press: 14 October 2010
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].
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- Copyright © Cambridge University Press 1996
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