Generalised Hausdorff measure of sets of Dirichlet non-improvable matrices in higher dimensions

Let psi : R+ -> R+ be a non-increasing function. A pair (A, b), where A is a real m x n matrix and b is an element of R-m, is said to be psi-Dirichlet improvable, if the system parallel to Aq + b - p parallel to(m) < psi (T), parallel to q parallel to(n) < T is solvable in p is an element of Z(m), q is an element of Z(n) for all sufficiently large T where parallel to center dot parallel to denotes the supremum norm. For psi-Dirichlet non-improvable sets, Kleinbock-Wadleigh (2019) proved the Lebesgue measure criterion whereas Kim-Kim (2022) established the Hausdorff measure results. In this paper we obtain the generalised Hausdorff f-measure version of Kim-Kim (2022) results for psi-Dirichlet non-improvable sets.