## Algebraic numbers and topologically equivalent measures in the Cantor set

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- by K. J. Huang
- Proc. Amer. Math. Soc.
**96**(1986), 560-562 - DOI: https://doi.org/10.1090/S0002-9939-1986-0826481-X
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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.## References

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## Bibliographic Information

- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**96**(1986), 560-562 - MSC: Primary 11R06; Secondary 28D99
- DOI: https://doi.org/10.1090/S0002-9939-1986-0826481-X
- MathSciNet review: 826481