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| The Borel measure of sequences with bounded run-length |
| AlisaDeStefano1,ClydeMartin2 |
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| (1 Department of Mathematics and Computer Science, College of the Holy Cross, 1 College St, Worcester, MA 01610, USA;2 Department of Mathematics and Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA) |
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| 摘要: |
| 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. |
| 关键词: Digitization · Borel measure · Binary sequences · Bounded run-length · Irrational flow · Torus |
| DOI：https://doi.org/10.1007/s11768-022-00102-1 |
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| 基金项目: |
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| The Borel measure of sequences with bounded run-length |
| Alisa DeStefano1,Clyde Martin2 |
| (1 Department of Mathematics and Computer Science, College of the Holy Cross, 1 College St, Worcester, MA 01610, USA;2 Department of Mathematics and Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA) |
| 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. |
| Key words: Digitization · Borel measure · Binary sequences · Bounded run-length · Irrational flow · Torus |
