Article
A Theorem of Khintchine Type
Authors
Abstract
Let ψ : N → [0, ∞) be an approximation function with
∑∞_{q=0} ψ(q) = ∞ and the property that there exists δ > 0 such that
ψ(q) ≥ δ ψ(s) for all q ∈ N and all s ∈ {q, q + 1, ..., 2q}. Then the set
{ x ∈ (0,1] : |x − p/q| < ψ(q)/q for infinitely many reduced rationals p/q } has Lebesgue measure one.
Keywords
Khintchine theorem, Borel–Cantelli lemma, approximation function, Euler’s φ function, Dawson–Sankoff inequality, Lebesgue measure, Duffin–Schaeffer conjecture.
Citation
Zoli, E. (2008). A theorem of khintchine type. Uniform Distribution Theory, 3(1), 73–83.
E. Zoli, “A theorem of khintchine type,” Uniform Distribution Theory, vol. 3, no. 1, pp. 73–83, 2008.
Zoli E. A theorem of khintchine type. Uniform Distribution Theory. 2008;3(1):73–83.
Zoli, E. (2008), ‘A theorem of khintchine type’, Uniform Distribution Theory, 3(1), pp. 73–83.
Zoli, Enrico. “A Theorem of Khintchine Type.” Uniform Distribution Theory, vol. 3, no. 1, 2008, pp. 73–83.
Zoli, Enrico. “A Theorem of Khintchine Type.” Uniform Distribution Theory 3, no. 1 (2008): 73–83.
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Published by: Engineering Journals
