OAI/MeasureTheory/Falconer/Recursion/UnitProfiles.lean

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7 declarations, 0 contain sorry, 0 declared as axioms

The constructed d-Lipschitz profiles on the unit interval

This is the paper's normalization of the finite-tree profile. Its slope bound is the ambient dimension d, and its values lie between zero and d.

  1. def OAI.Falconer.Regularization.unitProfile line 16
  2. theorem OAI.Falconer.Regularization.unitProfile_continuous line 20
  3. theorem OAI.Falconer.Regularization.unitProfile_zero line 24
  4. theorem OAI.Falconer.Regularization.unitProfile_increment line 28
  5. theorem OAI.Falconer.Regularization.unitProfile_monotoneOn line 41
  6. theorem OAI.Falconer.Regularization.unitProfile_lipschitzOn line 48
  7. theorem OAI.Falconer.Regularization.unitProfile_range line 62