OAI/MeasureTheory/Falconer/Estimates/LocalCellLines.lean

GitHub source file

10 declarations, 0 contain sorry, 0 declared as axioms

The exact line map for an isotropically rescaled point cell. It preserves the original line witnesses and their cardinalities; no direction thinning is needed for the elementary local incidence estimate.

  1. def OAI.Falconer.localCellLine line 13
  2. def OAI.Falconer.unlocalCellLine line 16
  3. theorem OAI.Falconer.localCellLine_leftInverse line 19
  4. theorem OAI.Falconer.localCellLine_rightInverse line 29
  5. theorem OAI.Falconer.localCellLine_injective line 39
  6. theorem OAI.Falconer.unlocalCellLine_dist line 43
  7. theorem OAI.Falconer.localCellLine_regular line 60
  8. theorem OAI.Falconer.localCellLine_residual line 85
  9. theorem OAI.Falconer.localCellLine_incident line 93
  10. theorem OAI.Falconer.localCellLine_chart line 103