Geodesic
On normal numbers mod $2$
Colloquium Mathematicum, Tome 76 (1998) no. 2, pp. 161-170
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It is proved that a real-valued function $f(x)=\exp(\pi i \chi_I(x))$, where I is an interval contained in [0,1), is not of the form $f(x)=\overline{q(2x)}q(x)$ with |q(x)|=1 a.e. if I has dyadic endpoints. A relation of this result to the uniform distribution mod 2 is also shown.
DOI : 10.4064/cm-76-2-161-170
Keywords: coboundary, metric density, normal number, uniform distribution 
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Youngho Ahn; Geon Choe. On normal numbers mod $2$. Colloquium Mathematicum, Tome 76 (1998) no. 2, pp. 161-170. doi: 10.4064/cm-76-2-161-170

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