It is well known that every x ∈ (0, 1] can be expanded to an infinite Lüroth series in the form of, where dn(x) ≥ 2 for all n ≥ 1. In this paper, sets of points with some restrictions on the digits in Lüroth series expansions are considered. Mainly, the Hausdorff dimensions of the Cantor sets Fφ ={ x ∈(0,1]:dn(x)≥ φ(n), ∀n ≥1} are completely determined, where φ is an integer-valued function defined on ℕ, and φ(n) → ∞ as n → ∞. © 2011 Institute of Mathematics of the Academy of Scienc...
