OAI/Analysis/LipschitzHilbert/Geometry/RectangleCountingEnergy.lean

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8 declarations, 0 contain sorry, 0 declared as axioms

Exact first and second moments of finite rectangle counts, in the normalization of Lacey--Li's covering lemma (3.1)--(3.2).

  1. def OAI.LipschitzHilbert.rectangleCount line 14
  2. theorem OAI.LipschitzHilbert.rectangleCount_measurable line 17
  3. theorem OAI.LipschitzHilbert.rectangleCount_first_moment line 21
  4. theorem OAI.LipschitzHilbert.rectangleCount_second_moment line 27
  5. theorem OAI.LipschitzHilbert.rectangleCount_first_moment_ne_top line 50
  6. theorem OAI.LipschitzHilbert.rectangleCount_second_moment_ne_top line 55
  7. theorem OAI.LipschitzHilbert.rectangleCount_pairing line 64
  8. theorem OAI.LipschitzHilbert.rectangleCount_pairing_sq_le line 79