DyadicRadialSummability.lean`

1 declarations, 0 contain sorry, 0 declared as axioms

Summable errors for the actual radial derivative and original covectors

theorem OAI.RegularPointCoordinates.dyadic_radial_fit_summability line 20

Source documentation

The actual distance replacements and the same dyadic normalizing frames give summable normalized squared fit errors. All analytic error terms are the original Poisson defect; no radial estimate is assumed.

theorem dyadic_radial_fit_summability {K : ℝ} (m : ℕ)
    (hX : NoncollapsedRCD K (m + 2) X) [IsFiniteMeasureOnCompacts (hausdorff (m + 2) X)]
    (hhessian : LocalPoissonHessianInput hX)
    {a κ r0 B J C A Cχ L δ : ℝ} {p : X}
    (ha : 0 ≤ a) (hκ : 0 ≤ κ) (hK : -κ ≤ K)
    (hB : 0 ≤ B) (hJ : 0 ≤ J) (hA : 0 ≤ A) (hCχ : 0 ≤ Cχ)
    (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