Abstract
We consider averages of continuous functions under the action of cellular automata, which were proposed by Boyle, Lind and Rudolph in 1988. It is proved that, at non-shift-periodic points, the averages converge point-wisely to the integration with respect to the uniform Bernoulli measure.
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Communicated by H. Bruin.
The authors are supported by the Fundamental Research Funds for the Central Universities of China (Grant No. 2012201020204), NSFC11171128 and 11271148.
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Liu, W., Ma, J. Limit averages of continuous functions under the action of cellular automata. Monatsh Math 181, 869–874 (2016). https://doi.org/10.1007/s00605-015-0869-6
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DOI: https://doi.org/10.1007/s00605-015-0869-6