Dilation of surviving excursion age measures

Continuous real tests preserve convergence in measure along countably generated filters. Time dilation and excursion scaling preserve null sets. Restricting their product to surviving bounded age windows gives the transfer needed for universal-subsequence limits.

theorem BGW.StableTrees.quasiMeasurePreserving_excursion_age_scale {θ : ℝ} (hθ : 1 < θ ∧ θ ≤ 2) (c : ↑(Set.Ioi 0)) (S : NNReal) : MeasureTheory.QuasiMeasurePreserving (fun (p : ℝ × Excursion) => (↑c * p.1, excursionScale θ c p.2)) (heightExcursionAgeMeasure θ S) (heightExcursionAgeMeasure θ ((↑c).toNNReal * S))

Joint age/mark dilation preserves null sets on the corresponding surviving age windows.