抄録
Let E be an interval in the unit interval [0, 1). For each x ∈ [0, 1) define dn (x) ∈ {0, 1} by dn(x):= ∑i=1n 1E({2i-1x}) (mod 2), where {t} is the fractional part of t. Then x is called a normal number mod 2 with respect to E if N-1 ∑n=1N dn (x) converges to 1/2. It is shown that for any interval E ≠ (1/6, 5/6) a.e. x is a normal number mod 2 with respect to E. For E = (1/6, 5/6) it is proved that N-1 ∑n=1N dn (x) converges a.e. and the limit equals 1/3 or 2/3 depending on x.
本文言語 | English |
---|---|
ページ(範囲) | 53-60 |
ページ数 | 8 |
ジャーナル | Studia Mathematica |
巻 | 165 |
号 | 1 |
DOI | |
出版ステータス | Published - 2004 |
ASJC Scopus subject areas
- 数学 (全般)