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Remarks on invariant measures for number theoretic transformations

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Abstract

A sufficient condition for the existence of an invariant measure is given that is useful in number theory. A connection with a problem of Blum is pointed out. Kuzmin's theorem is considered from an operator point of view, and the Chacon-Ornstein theorem is applied to give almost everywhere Cesaro convergence to the density of the invariant measure.

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Authors and Affiliations

  1. Department of Mathematics, Idaho State University, Pocatello, ID, 83201, USA

    Michael S. Waterman

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  1. Michael S. Waterman
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Additional information

This work was supported in part by National Science Foundation grants GP-28313 and GP-28313§1. The work was partly supported under the auspices of the U. S. Atomic Energy Commission while the author was a faculty participant of the Associated Western Universities at Los Alamos Scientific Laboratory.

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Waterman, M.S. Remarks on invariant measures for number theoretic transformations. Monatshefte fü Mathematik 79, 157–163 (1975). https://doi.org/10.1007/BF01585673

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