Abstract
We prove that for any s, t ⩾ 0 with s + t = 1 and any θ ∈ ℝ with infq∈ℕq1/s||qθ|| > 0, the set of y ∈ ℝ for which (θ, y) is (s, t)-badly approximable is ½-winning for Schmidt's game. As a consequence, we remove a technical assumption in a recent theorem of Badziahin–Pollington–Velani on simultaneous Diophantine approximation.
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