The Wiener Criterion at $\mathrm{\infty }$ for Degenerate Elliptic Equations

This paper establishes a Wiener criterion at $\mathrm{\infty }$ to characterise the unique solvability of the Dirichlet problem for degenerate elliptic equations with power-like weights in arbitrary open sets. In the measure-theoretical context, the criterion determines whether the $\text{A}$-harmonic measure of $\mathrm{\infty }$ is null or positive. From the topological point of view, it presents a test for the thinness of the exterior set at $\mathrm{\infty }$ in the $\text{A}$-fine topology.