The limit satisfies the transport weak form

theorem AVenhance.Infra.FullTheorem.TransportLimit.limit_weak_form {b : ℝ → Homogenization.Vec 2 → Homogenization.Vec 2} (h : DriftHyp b) {θ₀ : Homogenization.Vec 2 → ℝ} (hθ₀ : Homogenization.MemL2On unitCube θ₀) {κ : ℕ → ℝ} (hκ : ∀ (j : ℕ), 0 < κ j) (hκ0 : Filter.Tendsto κ Filter.atTop (nhds 0)) {θ : ℕ → ℝ → Homogenization.Vec 2 → ℝ} {Dθ : ℕ → ℝ → Homogenization.Vec 2 → Homogenization.Vec 2} (hu : ∀ (j : ℕ), IsWeakSolutionGrad b (κ j) θ₀ (θ j) (Dθ j)) {Θ : ℝ → Homogenization.Vec 2 → ℝ} (hΘ : MeasureTheory.MemLp (fun (p : ℝ × Homogenization.Vec 2) => Θ p.1 p.2) 2 (MeasureTheory.volume.restrict timeCube)) (hunif : ∀ (η : ℝ), 0 < η → ∃ (N : ℕ), ∀ j ≥ N, ∀ t ∈ Set.Icc 0 1, √(l2NormSq fun (x : Homogenization.Vec 2) => θ j t x - Θ t x) ≤ η) {φ : ℝ → Homogenization.Vec 2 → ℝ} (hφ : IsTestFunction φ) : MeasureTheory.Integrable (fun (p : ℝ × Homogenization.Vec 2) => Θ p.1 p.2 * Homogenization.vecDot (b p.1 p.2) (spaceGrad (φ p.1) p.2)) (MeasureTheory.volume.restrict timeCube) ∧ ∫ (p : ℝ × Homogenization.Vec 2) in timeCube, -Θ p.1 p.2 * deriv (fun (s : ℝ) => φ s p.2) p.1 - Θ p.1 p.2 * Homogenization.vecDot (b p.1 p.2) (spaceGrad (φ p.1) p.2) = ∫ (x : Homogenization.Vec 2) in unitCube, θ₀ x * φ 0 x