OAI/Analysis/RieszRectifiability/Projections/ProjectionCells.lean

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20 declarations, 0 contain sorry, 0 declared as axioms

Measures on parametrized boxes

Restricting Lebesgue measure to a finite box and pushing it forward through a parametrization defines the associated box-plane measure. Its finite-measure packaging allows these parametrized cells to enter weak-convergence arguments.

  1. def OAI.RieszRectifiability.boxPlaneMeasure line 24
  2. instance OAI.RieszRectifiability.(instance at line 27) line 27
  3. def OAI.RieszRectifiability.boxPlaneFiniteMeasure line 33
  4. theorem OAI.RieszRectifiability.boxPlaneMeasure_univ line 36
  5. theorem OAI.RieszRectifiability.boxPlaneFiniteMeasure_ne_zero line 41
  6. theorem OAI.RieszRectifiability.boxPlaneMeasure_preimage line 51
  7. def OAI.RieszRectifiability.dyadicProjectionCell line 61
  8. theorem OAI.RieszRectifiability.dyadicProjectionCell_measurable line 64
  9. theorem OAI.RieszRectifiability.dyadicProjectionCell_disjoint line 70
  10. theorem OAI.RieszRectifiability.dyadicProjectionCell_cover line 78
  11. theorem OAI.RieszRectifiability.dyadicProjectionCell_mass line 82
  12. theorem OAI.RieszRectifiability.boxPlaneMeasure_ae_coordinates line 95
  13. theorem OAI.RieszRectifiability.dyadicProjectionCell_cover_ae line 102
  14. theorem OAI.RieszRectifiability.dyadicProjectionCell_null_frontier line 110
  15. theorem OAI.RieszRectifiability.dyadicProjectionCell_dist_reference line 121
  16. theorem OAI.RieszRectifiability.boxPlaneMeasure_ae_section line 136
  17. theorem OAI.RieszRectifiability.dyadicProjectionCell_ae_dist_reference line 144
  18. theorem OAI.RieszRectifiability.dyadicProjectionCell_ae_diameter line 156
  19. theorem OAI.RieszRectifiability.dyadicProjectionCell_mass_tendsto line 173
  20. theorem OAI.RieszRectifiability.dyadicProjectionCell_eventual_mass_lower line 185