OAI/Analysis/RieszRectifiability/Foundations/TwoSidedIntrinsicDensity.lean

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Two-sided intrinsic densities

Lower ball-growth bounds give a positive multiple of Euclidean volume dominated by the measure. Together with the upper-growth domination, this produces a measurable density with pointwise lower and upper bounds by clipping its Radon–Nikodym derivative without changing the represented measure.

  1. def OAI.RieszRectifiability.intrinsicLowerDensityBound line 22
  2. theorem OAI.RieszRectifiability.intrinsicLowerDensityBound_pos line 25
  3. theorem OAI.RieszRectifiability.intrinsic_volume_le_of_lower_growth line 32
  4. theorem OAI.RieszRectifiability.nnreal_le_rnDeriv_of_domination line 63
  5. theorem OAI.RieszRectifiability.exists_two_sided_density_of_domination line 72
  6. theorem OAI.RieszRectifiability.exists_two_sided_intrinsic_density line 104