OAI/Geometry/RCD/Coordinates/MeasuredRescalingFromCoordinates.lean
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Measured rescaling convergence from fixed-ball estimates
The quantitative measured-coordinate input already controls every measurable pointed approximation. Measurable net replacement and the vanishing rescaled curvature therefore give its sequential formulation.
- theorem
OAI.RegularPointCoordinates.LocalMeasuredCoordinateInput.euclideanMeasuredRescalingConvergenceline 22Source documentation
The fixed-ball measured-coordinate theorem supplies the separately stated measured rescaling convergence, with no additional measure input.
theorem LocalMeasuredCoordinateInput.euclideanMeasuredRescalingConvergence {K : ℝ} {n : ℕ} {hX : NoncollapsedRCD K n X} (hinput : LocalMeasuredCoordinateInput hX) (hn : 2 ≤ n) (p : X) : EuclideanMeasuredRescalingConvergence (hausdorff n X) n p := by …Mentions: OAI.RegularPointCoordinates.NoncollapsedRCD, OAI.RegularPointCoordinates.LocalMeasuredCoordinateInput, OAI.RegularPointCoordinates.EuclideanMeasuredRescalingConvergence, OAI.RegularPointCoordinates.hausdorff