| import Mathlib | |
| namespace OAI | |
| noncomputable section | |
| open Set Filter | |
| open scoped Topology | |
| namespace WeakMTWTransport | |
| lemma diagonal_tendsto_of_close {X : Type*} [PseudoMetricSpace X] | |
| {f a : ℕ → X} {x : X} {ε : ℕ → ℝ} | |
| (ha : Tendsto a atTop (𝓝 x)) (hε : Tendsto ε atTop (𝓝 0)) | |
| (hclose : ∀ᶠ k in atTop,dist (f k) (a k)≤ε k) : Tendsto f atTop (𝓝 x) := by | |
| apply tendsto_of_tendsto_of_dist ha | |
| exact squeeze_zero' (Eventually.of_forall (fun _=>dist_nonneg)) (hclose.mono (fun k hk=>by simpa only [dist_comm] using hk)) hε | |
| end WeakMTWTransport | |
| end | |
| end OAI | |