OAI/Analysis/LipschitzHilbert/Trees/LineGridBMO.lean

GitHub source file

13 declarations, 0 contain sorry, 0 declared as axioms

Mean oscillation on the actual line cells controls every martingale jump by the branching factor. This supplies the overshoot bound in the dyadic stopping proof of John--Nirenberg.

  1. def OAI.LipschitzHilbert.FiniteLineGrid.cellMean line 16
  2. def OAI.LipschitzHilbert.FiniteLineGrid.HasMeanOscillationBound line 19
  3. instance OAI.LipschitzHilbert.FiniteLineGrid.cellMeasure_finite line 23
  4. theorem OAI.LipschitzHilbert.FiniteLineGrid.cell_mass line 28
  5. theorem OAI.LipschitzHilbert.FiniteLineGrid.cellMean_eq_integralAverage line 35
  6. theorem OAI.LipschitzHilbert.FiniteLineGrid.cellMean_sub_constant_le line 39
  7. theorem OAI.LipschitzHilbert.FiniteLineGrid.cell_subset_parent line 48
  8. theorem OAI.LipschitzHilbert.FiniteLineGrid.parent_index_lt line 59
  9. theorem OAI.LipschitzHilbert.FiniteLineGrid.meshWidth_succ line 64
  10. theorem OAI.LipschitzHilbert.FiniteLineGrid.cellMean_parent_jump line 68
  11. theorem OAI.LipschitzHilbert.FiniteLineGrid.average_eq_cellMean line 95
  12. theorem OAI.LipschitzHilbert.FiniteLineGrid.average_jump_le line 102
  13. theorem OAI.LipschitzHilbert.FiniteLineGrid.average_jump_le_everywhere line 116