Hausdorff dimension of an exceptional set in the theory of continued fractions**The research of A Bakhtawar is supported by La Trobe University postgraduate research award. The research of M Hussain is supported by La Trobe University startup grant and Australian Research Council Discovery Project (DP200100994).

Abstract

In this article we calculate the Hausdorff dimension of the setwhere is any function with limn→∞ Φ(n) = ∞. This in turn contributes to the metrical theory of continued fractions as well as gives insights about the set of Dirichlet non-improvable numbers.