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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Algebraic numbers and topologically equivalent measures in the Cantor set


Author: K. J. Huang
Journal: Proc. Amer. Math. Soc. 96 (1986), 560-562
MSC: Primary 11R06; Secondary 28D99
MathSciNet review: 826481
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Abstract: It is known that the transcendental and rational numbers in the unit interval are not binomial numbers. In this article we will show that the algebraic integers of degree 2 are not binomial numbers either. Therefore two shift invariant measures $ u(s),u(r)$ with $ r$ being an algebraic integer of degree 2 in the unit interval are topologically equivalent if and only if $ s = r$ or $ s = 1 - r$. We also show that for each positive integer $ n{\text{ > 2}}$, there are algebraic integers and fractionals of degree $ n$ in the unit interval that are binomial numbers.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0826481-X
PII: S 0002-9939(1986)0826481-X
Article copyright: © Copyright 1986 American Mathematical Society