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The Borel measure of sequences with bounded run-length

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Abstract

Infinite sequences defined with a finite alphabet are studied and it is shown that the set of sequences with bounded run-length has measure zero with respect to the Borel measure. Such sequences arise in many applications including digitization of certain linear systems involving flows on the circle and 2-torus, large scale simulation, and cryptology. They are basic objects of study in ergodic theory.

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Author notes

  1. Clyde Martin contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics and Computer Science, College of the Holy Cross, 1 College St, Worcester, MA, 01610, USA

    Alisa DeStefano

  2. Department of Mathematics and Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX, 79409, USA

    Clyde Martin

Authors
  1. Alisa DeStefano
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  2. Clyde Martin
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Correspondence to Alisa DeStefano.

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DeStefano, A., Martin, C. The Borel measure of sequences with bounded run-length. Control Theory Technol. 20, 316–322 (2022). https://doi.org/10.1007/s11768-022-00102-1

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  • DOI: https://doi.org/10.1007/s11768-022-00102-1

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