It is proved that a real-valued function , where I is an interval contained in [0,1), is not of the form 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.
@article{bwmeta1.element.bwnjournal-article-cmv76z2p161bwm, author = {Youngho Ahn and Geon Choe}, title = {On normal numbers mod $2$ }, journal = {Colloquium Mathematicae}, volume = {78}, year = {1998}, pages = {161-170}, zbl = {0892.11025}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv76z2p161bwm} }
Ahn, Youngho; Choe, Geon. On normal numbers mod $2$ . Colloquium Mathematicae, Tome 78 (1998) pp. 161-170. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv76z2p161bwm/
[000] [1] G. H. Choe, Spectral types of uniform distribution, Proc. Amer. Math. Soc. 120 (1994), 715-722. | Zbl 0803.11039
[001] [2] G. H. Choe, Ergodicity and irrational rotations, Proc. Roy. Irish Acad. 93A (1993), 193-202. | Zbl 0807.28009
[002] [3] R. B. Kirk, Sets which split families of measurable sets, Amer. Math. Monthly 79 (1972), 884-886. | Zbl 0249.28003
[003] [4] K. Petersen, Ergodic Theory, Cambridge Univ. Press, 1983.
[004] [5] W. Rudin, Real and Complex Analysis, McGraw-Hill, 1986.
[005] [6] W. A. Veech, Strict ergodicity in zero dimensional dynamical systems and the Kronecker-Weyl theorem mod , Trans. Amer. Math. Soc. 140 (1969), 1-33. | Zbl 0201.05601
[006] [7] P. Walters, An Introduction to Ergodic Theory, Springer, New York, 1982. | Zbl 0475.28009