On the Hausdorff Dimension of weighted exactly Approximable Vectors

Abstract

We show that the Hausdorff dimension of $\mathbf{w}$-weighted $\tau$-exactly approximable vectors in ${\mathbb{R}}^d$ coincides with the Hausdorff dimension of $\mathbf{w}$-weighted $\tau$-approximable vectors, generalizing a result of the first named author and De Saxcé.