Hausdorff measure Duffin–Schaeffer conjecture

Let $k\in\mathbb{N}$, let $f$ be a dimension function such that $r^{-k}f(r)$ is monotonic, and let $\mathcal{A}_k”(\psi)\subset[0,1]^k$ be the set of simultaneously reduced $\psi$-well approximable points. Let $\varphi$ denote Euler's totient function and let $\mathcal{H}^f$ be the Hausdorff $f$-measure. Hausdorff measure Duffin–Schaeffer conjecture. For every approximating function $\psi:\mathbb{N}\to\mathbb{R}_{\geq 0}$,

$$\mathcal{H}^f(\mathcal{A}_k”(\psi))=\begin{cases}0&\text{if }\displaystyle\sum_{q=1}^{\infty}f\left(\frac{\psi(q)}q\right)\varphi(q)^k<\infty,\\\\[2ex]\mathcal{H}^f([0,1]^k)&\text{if }\displaystyle\sum_{q=1}^{\infty}f\left(\frac{\psi(q)}q\right)\varphi(q)^k=\infty. \end{cases}$$

This is the Hausdorff-measure generalisation of the one-dimensional and higher-dimensional Duffin–Schaeffer conjectures presented by Beresnevich and Velani; the supplied text does not state whether it has been resolved in this full form.