OAI/Analysis/LipschitzHilbert/Trees/LineGridLimit.lean

GitHub source file

6 declarations, 0 contain sorry, 0 declared as axioms

Actual cell averages converge at every continuity point in the root. Only this continuous-function specialization of differentiation is needed for the finite smooth packet and variation functions.

  1. def OAI.LipschitzHilbert.FiniteLineGrid.withDepth line 17
  2. theorem OAI.LipschitzHilbert.FiniteLineGrid.cell_zero line 19
  3. theorem OAI.LipschitzHilbert.FiniteLineGrid.average_zero_eq_integralAverage line 23
  4. theorem OAI.LipschitzHilbert.FiniteLineGrid.average_close_of_mesh line 30
  5. theorem OAI.LipschitzHilbert.FiniteLineGrid.meshWidth_tendsto_zero line 56
  6. theorem OAI.LipschitzHilbert.FiniteLineGrid.average_tendsto_at_continuity line 67