The Borel measure of sequences with bounded run-length

Alisa DeStefano1, Clyde Martin2
1Department of Mathematics and Computer Science, College of The Holy Cross, Worcester, USA
2Department of Mathematics and Statistics, Texas Tech University, Lubbock, USA

Tóm tắt

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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