The weak inhomogeneous Duffin–Schaeffer conjecture of Catlin

Let $\gamma\in\mathbb{R}$, let $\psi:\mathbb{N}\to\mathbb{R}_{\geq 0}$, and let $E_q$ be the inhomogeneous approximation sets defined by

$$E_q=\left\{x\in[0,1]:\left|qx-a-\gamma\right|<\psi(q)\text{ for some }a\in\mathbb{Z}\right\}.$$

Weak inhomogeneous Duffin–Schaeffer conjecture. The condition denoted by

$$in the source holds. This is identified in the source as a weaker form of the inhomogeneous Duffin–Schaeffer statement and is attributed there to Conjecture 1.22 of the cited work. The supplied context does not reproduce$$

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