Hausdorff measure of sets of inhomogeneous Dirichlet non-improvable affine forms with weights

Under a reasonable decay assumption on the approximating function, we establish a zero-full law for the Hausdorff measure of sets of inhomogeneous Dirichlet non-improvable affine forms with weights, thereby answering a question posed by Kim and Kim (§5.3, Adv. Math., 2022).