Hausdorff measure of sets of Dirichlet non-improvable affine forms

Taehyeong Kim, Wooyeon Kim

For a decreasing real valued function $\psi$, a pair $(A,\mathbf{b})$ of a real $m\times n$ matrix $A$ and $\mathbf{b}\in {\mathbb{R}}^m$ is said to be $\psi$-Dirichlet improvable if the sy…