The generalised Hausdorff measure of sets of Dirichlet non-improvable numbers

Philip Bos, Mumtaz Hussain, David Simmons

Let $\psi :{\mathbb{R}}_{+}\to {\mathbb{R}}_{+}$ be a non-increasing function. A real number $x$ is said to be $\psi$-Dirichlet improvable if the system $$|qx-p|< \, ψ(t) \ \ {\text{and}} \ \ |q|<t$…