Normal equivalencies for eventually periodic basic sequences

作者：Airey Dylan; Mance Bill^*

来源：Indagationes Mathematicae, 2015, 26(3): 476-484.

DOI：10.1016/j.indag.2015.02.002

• Normal numbers
• Cantor series
• Normal equivalencies

Researchers such as W.M. Schmidt, A.D. Pollington, and F. Schweiger have studied when normality with respect to one expansion is equivalent to normality with respect to another expansion. Following in their footsteps, we show that when Q is an eventually periodic basic sequence, that Q-normality and Q-distribution normality are equivalent to normality in base b where b is dependent on Q. We also show that boundedness of the basic sequence is not sufficient for this equivalence.

• 出版日期2015-5