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

Abstract

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).

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