OAI/Analysis/AffineBernstein/AffineImageCoordinates.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

1. lemma OAI.AffineBernstein.continuousAffineEquiv_decomposition line 18
2. lemma OAI.AffineBernstein.continuousAffineEquiv_inverse_decomposition line 23
3. theorem OAI.AffineBernstein.InAffineLimitFamily.epigraph_pullback_approximation line 34

   Source documentation

   Rewrite the actual affine-image sequence in the exact pullback coordinates used throughout the PDE support estimates.

   theorem InAffineLimitFamily.epigraph_pullback_approximation {n k m : ℕ}
       {Ω : Set (Space n)} {u : Space n → ℝ} {C : Set (Space k × Space m)}
       (hf : InAffineLimitFamily (sourceEpigraph Ω u) C) :
       ∃ a : ℕ → Space n × ℝ, ∃ L : ℕ → (Space k × Space m) ≃L[ℝ] (Space n × ℝ),
         LocalDistanceConverges (fun j => affineEpigraphPullback Ω u (a j) (L j)) C := by
   …

   Mentions: OAI.AffineBernstein.Space, OAI.AffineBernstein.InAffineLimitFamily, OAI.AffineBernstein.sourceEpigraph, OAI.AffineBernstein.LocalDistanceConverges, OAI.AffineBernstein.affineEpigraphPullback