UniformRadialSummability.lean`

1 declarations, 0 contain sorry, 0 declared as axioms

A uniform envelope constant for all actual radial fits

theorem OAI.RegularPointCoordinates.dyadic_radial_fit_summability_uniform line 17

Source documentation

Fix the radial contraction constant before choosing the root, center, map, and size of the splitting error.

theorem dyadic_radial_fit_summability_uniform {K : ℝ} (m : ℕ)
    (hX : NoncollapsedRCD K (m + 2) X) [IsFiniteMeasureOnCompacts (hausdorff (m + 2) X)]
    (hhessian : LocalPoissonHessianInput hX) {B J A Cχ : ℝ} {d : ℕ}
    (hB : 0 ≤ B) (hJ : 0 ≤ J) (hA : 0 ≤ A) (hCχ : 0 ≤ Cχ) (hd : 0 < d) :
    ∃ Z : ℝ, 0 < Z ∧ ∀ {a κ r0 C L δ : ℝ} {p : X},
    ∀ (_ha : 0 ≤ a) (_hκ : 0 ≤ κ) (_hK : -κ ≤ K)
    (_hr01 : r0 ≤ 1) (_hscale : a * (3 * r0) ≤ 1)
    (_hBG : BallVolumeComparison (hausdorff (m + 2) X) (comparisonModelVolume (m + 1) a))
    (S : DyadicDistanceSources (hausdorff (m + 2) X) hX.quadratic (m + 2) κ p r0)
    (T : DyadicDistanceReplacements (hausdorff (m + 2) X) hX.quadratic S B J C)
    (_hP : Summable (normalizedPoissonDefect (hausdorff (m + 2) X) hX.quadratic S))
    (_hquarter : ∀ t : ℝ, 0 < t → t ≤ r0 →
…

Mentions: OAI.RegularPointCoordinates.NoncollapsedRCD, OAI.RegularPointCoordinates.hausdorff, OAI.RegularPointCoordinates.LocalPoissonHessianInput, OAI.RegularPointCoordinates.BallVolumeComparison, OAI.RegularPointCoordinates.comparisonModelVolume, OAI.RegularPointCoordinates.DyadicDistanceSources, OAI.RegularPointCoordinates.DyadicDistanceReplacements, OAI.RegularPointCoordinates.normalizedPoissonDefect