Claims

../

1979_12_01_pollington: Pollington's Theorem: for every sequence with consecutive ratios at least alpha > 1 there are beta > 0 and uncountably many xi with every fractional part of xi t_k in [beta, 1 - beta]; an irrational xi answers Problem 464.

1980_09_01_de_mathan: De Mathan's Corollary 1: for every sequence with consecutive ratios at least lambda > 1, the x of an interval with (q_n x) not everywhere dense mod 1 form a set of Hausdorff dimension 1; an irrational one answers Problem 464.

2001_04_01_katznelson: Katznelson's Theorem 1.2 and Claim 2: for a lacunary sequence the multipliers alpha keeping every lambda alpha away from the integers form a set of Hausdorff dimension 1; an irrational one answers Problem 464.

---