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 with being an algebraic integer of degree 2 in the unit interval are topologically equivalent if and only if or . We also show that for each positive integer , there are algebraic integers and fractionals of degree in the unit interval that are binomial numbers.

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DOI:
https://doi.org/10.1090/S0002-9939-1986-0826481-X

Article copyright:
© Copyright 1986
American Mathematical Society