OAI/Analysis/RieszRectifiability/Kernel/RieszPairingIdentification.lean

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Scalar Riesz pairings and affine normal heights

Pairing the Riesz kernel with a fixed normal identifies its interior contribution with the fractional bilinear form. For mean-zero tests, the exterior correction integrates to zero, identifying the scalar Riesz pairing with the normal cutoff pairing.

  1. def OAI.RieszRectifiability.affineNormalHeight line 21
  2. theorem OAI.RieszRectifiability.affineNormalHeight_difference line 24
  3. theorem OAI.RieszRectifiability.affineNormalHeight_lipschitz line 29
  4. theorem OAI.RieszRectifiability.kernel_inner_normal_difference line 37
  5. def OAI.RieszRectifiability.rieszInteriorIntegrand line 44
  6. def OAI.RieszRectifiability.rieszFarIntegrand line 48
  7. def OAI.RieszRectifiability.rieszScalarPairing line 52
  8. theorem OAI.RieszRectifiability.rieszInteriorIntegrand_eq_fractionalBilinear line 58
  9. theorem OAI.RieszRectifiability.rieszFarIntegrand_eq_normal_sub_correction line 66
  10. theorem OAI.RieszRectifiability.riesz_far_integral_eq_normal line 76
  11. theorem OAI.RieszRectifiability.normalCutoffPairing_eq_rieszScalarPairing line 96