The union-measure form of the Duffin–Schaeffer conjecture

For a non-negative function $\psi:\mathbb{N}\to\mathbb{R}$, let ${\mathcal E}_n(\psi)$ and $W(\psi)$ be as above, and define

$$Z(\psi)=\bigcup_{n=1}^{\infty}{\mathcal E}_n(\psi).$$

Let $\lambda$ denote Lebesgue measure on $\mathbb{R}/\mathbb{Z}$ and let $\varphi$ be Euler's phi function. Union-measure Duffin–Schaeffer conjecture. There exists a universal constant $C>0$ such that

\lambda(Z(\psi))\geq C\min\left\\{\sum_{n=1}^{\infty}\frac{\psi(n)\varphi(n)}{n},1\right\\}.

The paper proves that this formulation is equivalent to the classical Duffin–Schaeffer conjecture, so it remains open in the source.