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.

  1. theorem OAI.RegularPointCoordinates.LocalMeasuredCoordinateInput.euclideanMeasuredRescalingConvergence line 22

    Source 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